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tupdate documentation - sphere - GPU-based 3D discrete element method algorithm… |
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git clone git://src.adamsgaard.dk/sphere |
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Log |
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Files |
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Refs |
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LICENSE |
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--- |
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commit 81d7b44047babc963125026004031b612e6de13d |
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parent 0d5bba5c16a5ad5a76f908a2f082722e3d869c34 |
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Author: Anders Damsgaard <[email protected]> |
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Date: Thu, 7 Sep 2017 17:25:14 -0700 |
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update documentation |
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Diffstat: |
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M doc/html/.buildinfo | 2 +- |
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M doc/html/_sources/introduction.txt | 13 +++++-------- |
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M doc/html/cfd.html | 196 ++++++++++++++++-------------… |
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M doc/html/dem.html | 86 +++++++++++++++--------------- |
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M doc/html/genindex.html | 10 +++++----- |
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M doc/html/index.html | 10 +++++----- |
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M doc/html/introduction.html | 28 +++++++++++++--------------- |
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M doc/html/objects.inv | 0 |
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M doc/html/py-modindex.html | 10 +++++----- |
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M doc/html/python_api.html | 22 ++++++++++++++++------ |
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M doc/html/search.html | 10 +++++----- |
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M doc/html/searchindex.js | 4 ++-- |
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M doc/html/sphere_internals.html | 14 +++++++------- |
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M doc/pdf/sphere.pdf | 0 |
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M doc/sphinx/conf.py | 9 ++++++--- |
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M doc/sphinx/introduction.rst | 13 +++++-------- |
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M src/main.cpp | 4 ++-- |
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17 files changed, 218 insertions(+), 213 deletions(-) |
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--- |
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diff --git a/doc/html/.buildinfo b/doc/html/.buildinfo |
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t@@ -1,4 +1,4 @@ |
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# Sphinx build info version 1 |
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# This file hashes the configuration used when building these files. When it i… |
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-config: fe70a33065653dc9f13fbefebe7ac2f6 |
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+config: f6a3bc901e2eb5ac86d94b7ac7732d4c |
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tags: 645f666f9bcd5a90fca523b33c5a78b7 |
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diff --git a/doc/html/_sources/introduction.txt b/doc/html/_sources/introductio… |
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t@@ -132,9 +132,11 @@ from the root directory:: |
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$ cmake . && make |
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-NOTE: If your system does not have a GCC compiler (e.g. GCC-5 for CUDA 8) |
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-compatible with the installed CUDA version, try using ``clang-3.8`` instead:: |
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+NOTE: If your system does not have a GCC compiler compatible with the installed |
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+CUDA version (e.g. GCC-5 for CUDA 8), you will see errors at the linker stage.… |
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+In that case, try using ``clang-3.8`` as the C and C++ compiler instead:: |
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|
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+ $ rm -rf CMakeCache.txt CMakeFiles/ |
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$ export CC=$(which clang-3.8) && export CXX=$(which clang++-3.8) && cmake . … |
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After a successfull installation, the ``sphere`` executable will be located |
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t@@ -157,10 +159,6 @@ The output should look similar to this: |
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.. program-output:: ../../sphere --version |
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-The build can be verified by running a number of automated tests:: |
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- |
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- $ make test |
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- |
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The documentation can be read in the `reStructuredText |
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<http://docutils.sourceforge.net/docs/ref/rst/restructuredtext.html>`_-format … |
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the ``doc/sphinx/`` folder, or in the HTML or PDF formats in the folders |
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t@@ -193,10 +191,9 @@ After compiling the ``sphere`` binary, the procedure of a… |
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a simulation is typically arranged in the following order: |
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* Setup of particle assemblage, physical properties and conditions using the |
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- Python API. |
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+ Python API (``python/sphere.py``). |
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* Execution of ``sphere`` software, which simulates the particle behavior as… |
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function of time, as a result of the conditions initially specified in the |
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input file. |
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* Inspection, analysis, interpretation and visualization of ``sphere`` output |
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in Python, and/or scene rendering using the built-in ray tracer. |
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- |
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diff --git a/doc/html/cfd.html b/doc/html/cfd.html |
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t@@ -6,7 +6,7 @@ |
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<head> |
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
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- <title>Fluid simulation and particle-fluid interaction — sphere 1.00… |
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+ <title>Fluid simulation and particle-fluid interaction — sphere 2.15… |
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|
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<link rel="stylesheet" href="_static/classic.css" type="text/css" /> |
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<link rel="stylesheet" href="_static/pygments.css" type="text/css" /> |
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t@@ -14,7 +14,7 @@ |
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<script type="text/javascript"> |
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var DOCUMENTATION_OPTIONS = { |
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URL_ROOT: './', |
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- VERSION: '1.00-alpha', |
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+ VERSION: '2.15-beta', |
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COLLAPSE_INDEX: false, |
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FILE_SUFFIX: '.html', |
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HAS_SOURCE: true |
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t@@ -25,7 +25,7 @@ |
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<script type="text/javascript" src="_static/doctools.js"></script> |
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<link rel="index" title="Index" href="genindex.html" /> |
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<link rel="search" title="Search" href="search.html" /> |
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- <link rel="top" title="sphere 1.00-alpha documentation" href="index.html" … |
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+ <link rel="top" title="sphere 2.15-beta documentation" href="index.html" /> |
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<link rel="next" title="Python API" href="python_api.html" /> |
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<link rel="prev" title="Discrete element method" href="dem.html" /> |
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</head> |
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t@@ -45,7 +45,7 @@ |
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<li class="right" > |
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<a href="dem.html" title="Discrete element method" |
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accesskey="P">previous</a> |</li> |
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- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
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+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
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</ul> |
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</div> |
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t@@ -68,31 +68,31 @@ solution procedure and the numerical implementation.</p> |
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<p>Following the outline presented by <a class="reference external" href="http… |
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continuity equation for an incompressible fluid material is given by:</p> |
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<div class="math"> |
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-<p><img src="_images/math/341e857d6da62b73593a73dea371b22a955fd8e9.png" alt="\… |
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+<p><img src="_images/math/12f7f7910a11a5fc522425b33139287524c6e643.png" alt="\… |
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</div><p>and the momentum equation:</p> |
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<div class="math"> |
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-<p><img src="_images/math/f4c62b9c99051d7d2ca2b222af4b3394d02e1b1d.png" alt="\… |
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+<p><img src="_images/math/8b081782b6d73a048e968995b8605086e2c9ff1f.png" alt="\… |
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+ \rho (\boldsymbol{v} \cdot \nabla \boldsymbol{v}) |
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= \nabla \cdot \boldsymbol{\sigma} |
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- \boldsymbol{f}^i |
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+ \rho \boldsymbol{g}"/></p> |
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-</div><p>Here, <img class="math" src="_images/math/c8e734bf3818506e254ebfa3504… |
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-fluid density, <img class="math" src="_images/math/b4104067dcc504da8eada069712… |
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-<img class="math" src="_images/math/3ac346ec0a0efeed60827b2d73c5776cf4605902.p… |
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-<img class="math" src="_images/math/af2f4149a102bb8a3d74e9afbfd0d21b4c2f7084.p… |
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+</div><p>Here, <img class="math" src="_images/math/e7b48cd405b36440e40f970237c… |
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+fluid density, <img class="math" src="_images/math/2c6c8b6b1866df63a964f3c153a… |
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+<img class="math" src="_images/math/af5ed4f2edd188dadef68b3626d9fe7328f44848.p… |
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+<img class="math" src="_images/math/2be557ceeacba6f01feedb2ed907af87442104a1.p… |
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Newtonian fluids, the Cauchy stress is given by:</p> |
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<div class="math"> |
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-<p><img src="_images/math/9cb510f5a23b8a2cf167578e3197615a3cab7510.png" alt="\… |
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-</div><p><img class="math" src="_images/math/3eca8557203e86160952e1c0f735f7417… |
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-tensor, and <img class="math" src="_images/math/e29be0a3b86507644c82abbc0adfcb… |
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+<p><img src="_images/math/778cdde6b1b06e6e1e0c059db34e1821a0744b5b.png" alt="\… |
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+</div><p><img class="math" src="_images/math/27d463da4622be5b3ef1d4176ced7d7a3… |
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+tensor, and <img class="math" src="_images/math/ecff587acb289da44784794a8cbe92… |
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by:</p> |
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<div class="math"> |
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-<p><img src="_images/math/2ac5fed54f92fbc94d2fefb2aa5f17a1e326282e.png" alt="\… |
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+<p><img src="_images/math/048aa5b140cc86095a635258ba222f4ce562c46c.png" alt="\… |
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\mu_f \nabla \boldsymbol{v} |
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+ \mu_f (\nabla \boldsymbol{v})^T"/></p> |
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</div><p>By using the following vector identities:</p> |
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<div class="math"> |
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-<p><img src="_images/math/ffe6c17031ff1e2333c5bdc57773967dda2bebcc.png" alt="\… |
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+<p><img src="_images/math/54c6ba63db4b565c0d31fd9e64caae2e0990706b.png" alt="\… |
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|
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\nabla \cdot (\nabla \boldsymbol{v}) = \nabla^2 \boldsymbol{v} |
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t@@ -101,29 +101,29 @@ by:</p> |
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</div><p>the deviatoric component of the Cauchy stress tensor simplifies to the |
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following, assuming that spatial variations in the viscosity can be neglected:… |
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<div class="math"> |
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-<p><img src="_images/math/f220cc08054c66b15757b7073edbbfe33c2736e6.png" alt="=… |
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+<p><img src="_images/math/3b48976b9058ec32db3d413cfccaede0cd1bf31b.png" alt="=… |
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+ \mu_f \nabla^2 \boldsymbol{v}"/></p> |
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</div><p>Since we are dealing with fluid flow in a porous medium, additional t… |
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introduced to the equations for conservation of mass and momentum. In the |
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following, the equations are derived for the first spatial component. The |
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solution for the other components is trivial.</p> |
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<p>The porosity value (in the saturated porous medium the volumetric fraction … |
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-the fluid phase) denoted <img class="math" src="_images/math/10e009bdb83f96c5f… |
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+the fluid phase) denoted <img class="math" src="_images/math/c2f31c22645274c37… |
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momentum equations. The continuity equation becomes:</p> |
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<div class="math"> |
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-<p><img src="_images/math/6875433152b8a1a1624c131527286ababd8a8462.png" alt="\… |
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+<p><img src="_images/math/ccd454c154f50b005e2c673771bf6f7fc20dcdcd.png" alt="\… |
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+ \nabla \cdot (\phi \boldsymbol{v}) = 0"/></p> |
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-</div><p>For the <img class="math" src="_images/math/188c175aac0a8a9c224993367… |
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-with a body force <img class="math" src="_images/math/ce4f41d90f3fea6e5313ad3c… |
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+</div><p>For the <img class="math" src="_images/math/a59f68a4202623bb859a7093f… |
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+with a body force <img class="math" src="_images/math/0d2439f09c0757d8e087ec31… |
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<div class="math"> |
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-<p><img src="_images/math/60290a944b15183b06237a1483946560e640e1bf.png" alt="\… |
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+<p><img src="_images/math/94cb90a2611b5dcea79f236933ff4f759fddbe71.png" alt="\… |
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= \frac{1}{\rho} \left[ \nabla \cdot (\phi \boldsymbol{\sigma}) \right]_x |
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- \frac{1}{\rho} f^i_x |
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+ \phi g"/></p> |
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</div><p>In the Eulerian formulation, an advection term is added, and the Cauc… |
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tensor is represented as isotropic and deviatoric components individually:</p> |
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<div class="math"> |
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-<p><img src="_images/math/b991196699db1cde269ad006f427d8168fcfd679.png" alt="\… |
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+<p><img src="_images/math/30db4313208df84c2ad59bb33fb8d7cda1ea18ac.png" alt="\… |
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+ \boldsymbol{v} \cdot \nabla (\phi v_x) |
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= \frac{1}{\rho} \left[ \nabla \cdot (-\phi p \boldsymbol{I}) |
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+ \phi \boldsymbol{\tau}) \right]_x |
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t@@ -132,7 +132,7 @@ tensor is represented as isotropic and deviatoric componen… |
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</div><p>Using vector identities to rewrite the advection term, and expanding … |
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stress tensor term:</p> |
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<div class="math"> |
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-<p><img src="_images/math/a85779399f71d0d2d7fd373c5c5f2b572cf3bfd7.png" alt="\… |
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+<p><img src="_images/math/dfc197cc1f3569837c89d6fd4eda57f135c1941a.png" alt="\… |
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+ \nabla \cdot (\phi v_x \boldsymbol{v}) |
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- \phi v_x (\nabla \cdot \boldsymbol{v}) |
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= \frac{1}{\rho} \left[ -\nabla \phi p \right]_x |
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t@@ -141,24 +141,24 @@ stress tensor term:</p> |
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+ \phi g_x"/></p> |
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</div><p>Spatial variations in the porosity are neglected,</p> |
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<div class="math"> |
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-<p><img src="_images/math/249fc7f1e5fa5aa23b21d1fdf32ed10f0fcef400.png" alt="\… |
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+<p><img src="_images/math/f986f0b44e081477adec302df83930cdd31e5a42.png" alt="\… |
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</div><p>and the pressure is attributed to the fluid phase alone (model B in Z… |
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2007 and Zhou et al. 2010). The divergence of fluid velocities is defined to be |
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zero:</p> |
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<div class="math"> |
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-<p><img src="_images/math/96df96ab11be34dbe17cb0837626b7cc2772013e.png" alt="\… |
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+<p><img src="_images/math/bb89d2c54178c6063bbddbc2ef5cc575a6ad20d6.png" alt="\… |
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</div><p>With these assumptions, the momentum equation simplifies to:</p> |
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<div class="math"> |
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-<p><img src="_images/math/e58aec0a9dc37c78b74f5c34874ff852d8839f43.png" alt="\… |
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+<p><img src="_images/math/0c167e8743c59960431a47f16ee7244f2a13028f.png" alt="\… |
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+ \nabla \cdot (\phi v_x \boldsymbol{v}) |
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= -\frac{1}{\rho} \frac{\partial p}{\partial x} |
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+ \frac{1}{\rho} \left[ \nabla \cdot (\phi \boldsymbol{\tau}) \right]_x |
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- \frac{1}{\rho} f^i_x |
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+ \phi g_x"/></p> |
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-</div><p>The remaining part of the advection term is for the <img class="math"… |
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+</div><p>The remaining part of the advection term is for the <img class="math"… |
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found as:</p> |
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<div class="math"> |
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-<p><img src="_images/math/8bd85c906906e83dd3471973969959e831d271d7.png" alt="\… |
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+<p><img src="_images/math/145ab6190ce7c0c86da9eda1e2fac70f23b3a5fd.png" alt="\… |
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\left[ |
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\frac{\partial}{\partial x}, |
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\frac{\partial}{\partial y}, |
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t@@ -175,10 +175,10 @@ found as:</p> |
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\frac{\partial (\phi v_x v_x)}{\partial x} + |
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\frac{\partial (\phi v_x v_y)}{\partial y} + |
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\frac{\partial (\phi v_x v_z)}{\partial z}"/></p> |
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-</div><p>The deviatoric stress tensor is in this case symmetrical, i.e. <img c… |
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+</div><p>The deviatoric stress tensor is in this case symmetrical, i.e. <img c… |
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= \tau_{ji}"/>, and is found by:</p> |
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<div class="math"> |
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-<p><img src="_images/math/66dc70aa131124c6f87d7f2cbb96350d8b0397b9.png" alt="\… |
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+<p><img src="_images/math/0e293ff1406db52958abdce04458871a8a4c966f.png" alt="\… |
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= \frac{1}{\rho} |
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\left[ |
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\left[ |
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t@@ -217,17 +217,17 @@ found as:</p> |
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+ \frac{\partial (\phi \tau_{xz})}{\partial z} |
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\right)"/></p> |
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</div><p>In a linear viscous fluid, the stress and strain rate |
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-(<img class="math" src="_images/math/1ee5b5b2fe535711338cab9fde51ba86968186e2.… |
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-viscosity parameter <img class="math" src="_images/math/a1a25b9ae9dc5911e30e15… |
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+(<img class="math" src="_images/math/bdf1f5aad7dd65124011111a75c2b8b6c3252f0f.… |
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+viscosity parameter <img class="math" src="_images/math/d24e1c9504f0a7305bbf80… |
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<div class="math"> |
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-<p><img src="_images/math/2133ec642b2fa2a0bdc0612dc9080df18f64da53.png" alt="\… |
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+<p><img src="_images/math/f08a1f9bfdf41e9a3f9852b0aeae4a16500bb993.png" alt="\… |
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= \mu_f \left( |
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\frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i} |
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\right)"/></p> |
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</div><p>With this relationship, the deviatoric stress tensor components can be |
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calculated as:</p> |
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<div class="math"> |
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-<p><img src="_images/math/4d94b19a340ed5d6cfc3285e3c0678be914c3834.png" alt="\… |
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+<p><img src="_images/math/5fe663ae852d5c4d779d8d7827ca30a28852936a.png" alt="\… |
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\tau_{yy} = 2 \mu_f \frac{\partial v_y}{\partial y} \qquad |
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\tau_{zz} = 2 \mu_f \frac{\partial v_z}{\partial z} |
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|
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t@@ -239,26 +239,26 @@ calculated as:</p> |
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|
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\tau_{yz} = \mu_f \left( |
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\frac{\partial v_y}{\partial z} + \frac{\partial v_z}{\partial y} \right)"/></… |
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-</div><p>where <img class="math" src="_images/math/a1a25b9ae9dc5911e30e15d5ca2… |
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+</div><p>where <img class="math" src="_images/math/d24e1c9504f0a7305bbf80f4d75… |
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fluid rheology assumes identical bulk and shear viscosities. The derivation of |
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the equations for the other spatial components is trivial.</p> |
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</div> |
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<div class="section" id="porosity-estimation"> |
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<h2>Porosity estimation<a class="headerlink" href="#porosity-estimation" title… |
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<p>The solid volume in each fluid cell is determined by the ratio of the |
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-a cell-centered spherical cell volume (<img class="math" src="_images/math/db9… |
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-particle volumes (<img class="math" src="_images/math/754decd655584a824e0979fc… |
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-<img class="math" src="_images/math/13e4be57cf47de5302fc2e1746d965a6ee0f332c.p… |
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+a cell-centered spherical cell volume (<img class="math" src="_images/math/f99… |
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+particle volumes (<img class="math" src="_images/math/5bd22601fda700e6f36ba7e9… |
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+<img class="math" src="_images/math/5e8dd49b345fe138a2dacb54663b30b69335b6e6.p… |
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the fluid cell width. The nearby particles are characterized by position |
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-<img class="math" src="_images/math/ec1ce56da06483e62a9456229761ff166b345ed2.p… |
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+<img class="math" src="_images/math/1165d3ed99998c0f1ab1f9f25b42757182923a8b.p… |
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as:</p> |
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<div class="math"> |
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-<p><img src="_images/math/68f7c3ca449a28047e11af58f55b159b3156685c.png" alt="d… |
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+<p><img src="_images/math/3c39d664a1a005333c2e2e6088465ca5aabbc861.png" alt="d… |
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</div><p>The common volume of the two intersecting spheres is zero if the volu… |
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intersecting, lens shaped if they are intersecting, and spherical if the |
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particle is fully contained by the spherical cell volume:</p> |
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<div class="math"> |
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-<p><img src="_images/math/2b8b39498e0fa8ab6324f088a2330d47ef18cbd5.png" alt="V… |
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+<p><img src="_images/math/53e472051fcf13e3695e33c0f473e8d2c64f6ca7.png" alt="V… |
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\begin{cases} |
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0 & \textit{if } R_i + r_j \leq d_{ij} \\ |
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\frac{1}{12d_{ij}} \left[ \pi (R_i + r_j - d_{ij})^2 |
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t@@ -268,7 +268,7 @@ particle is fully contained by the spherical cell volume:<… |
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\end{cases}"/></p> |
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</div><p>Using this method, the cell porosity values are continuous through ti… |
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particles enter and exit the cell volume. The rate of porosity change |
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-(<img class="math" src="_images/math/de27eb4f973d27763dc4d176bf2453607ecaae42.… |
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+(<img class="math" src="_images/math/778cd9f6a1fa43976de0f124e625d935cf4c5f43.… |
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by considering the previous and current porosity.</p> |
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</div> |
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<div class="section" id="particle-fluid-interaction"> |
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t@@ -280,53 +280,53 @@ semi-empirical relationships. The drag force scales line… |
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difference in velocity between the fluid and particle phase. On the base of |
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Newton’s third law, the resulting drag force is applied with opposite si… |
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the particle and fluid.</p> |
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-<p>For fluid cells with porosities (<img class="math" src="_images/math/10e009… |
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+<p>For fluid cells with porosities (<img class="math" src="_images/math/c2f31c… |
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force is based on the Ergun (1952) equation:</p> |
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<div class="math"> |
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-<p><img src="_images/math/c65c93ecc36954688972785ecbae82a6d7a14a3a.png" alt="\… |
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+<p><img src="_images/math/86705dc922462e20080973641e4bcf0246476b94.png" alt="\… |
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150 \frac{\mu_f (1-\phi)^2}{\phi\bar{d}^2} |
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+ 1.75 \frac{(1-\phi)\rho_f |
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||\boldsymbol{v}_f - \bar{\boldsymbol{v}}_p||}{\bar{d}} |
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\right) |
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(\boldsymbol{v}_f - \bar{\boldsymbol{v}}_p)"/></p> |
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-</div><p>here, <img class="math" src="_images/math/082bced08237667a772227c2e3e… |
|
-<img class="math" src="_images/math/22b6d9dab340bfe13993da20589e4720449fe391.p… |
|
-<img class="math" src="_images/math/5b7072008fcf4dedaeed4d537fe5c808adedb826.p… |
|
+</div><p>here, <img class="math" src="_images/math/22474828ed1ac7525699de27914… |
|
+<img class="math" src="_images/math/35a936dcbe9d44868273ba50e463cc18afa0f108.p… |
|
+<img class="math" src="_images/math/ee125b2b5874be1ce504888dd7d7fa42b65e9261.p… |
|
particles in contact with the previously mentioned cell-centered sphere for |
|
porosity estimation contribute to the average particle velocity and diameter in |
|
the fluid cell.</p> |
|
<p>If the porosity is greater than 0.8, the cell-averaged drag force |
|
-(<img class="math" src="_images/math/fa8a7b2fb896adf1c9f17077664691e511aeb8e5.… |
|
+(<img class="math" src="_images/math/7dcc7d011290597e0833cc160b66996c5d9d4595.… |
|
which considers the fluid flow situation:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/0949063a26c6869766d571d13e61cf78f3a38c06.png" alt="\… |
|
+<p><img src="_images/math/75a974365e0604c0e8675dc2543166a1216a324e.png" alt="\… |
|
\frac{3}{4} |
|
\frac{C_d (1-\phi) \phi^{-2.65} \mu_f \rho_f |
|
||\boldsymbol{v}_f - \bar{\boldsymbol{v}}_p||}{\bar{d}} |
|
\right) |
|
(\boldsymbol{v}_f - \bar{\boldsymbol{v}}_p)"/></p> |
|
-</div><p>The drag coefficient <img class="math" src="_images/math/1beccd9a659c… |
|
-Reynolds number <img class="math" src="_images/math/0e0f0c7e69e0f315aed6d1762a… |
|
+</div><p>The drag coefficient <img class="math" src="_images/math/15746e47c01e… |
|
+Reynolds number <img class="math" src="_images/math/e7d45090e3dbe0db821c4e5fdf… |
|
<div class="math"> |
|
-<p><img src="_images/math/e2872fb63d995fa1112c468dcb10669c69795aef.png" alt="C… |
|
+<p><img src="_images/math/5962c6c4e4e193ec5e6b17320744252e30a86315.png" alt="C… |
|
\begin{cases} |
|
\frac{24}{Re} (1+0.15 (Re)^{0.687} & \textit{if } Re < 1,000 \\ |
|
0.44 & \textit{if } Re \geq 1,000 |
|
\end{cases}"/></p> |
|
</div><p>where the Reynold’s number is found by:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/f4bf201ecead6e3486688493ab1b1e82c39d93df.png" alt="R… |
|
+<p><img src="_images/math/8be75291f64c7dd21b34613d8a5346f3b9aff877.png" alt="R… |
|
||\boldsymbol{v}_f - \bar{\boldsymbol{v}}_p||"/></p> |
|
</div><p>The interaction force is applied to the fluid with negative sign as a |
|
-contribution to the body force <img class="math" src="_images/math/ce4f41d90f3… |
|
+contribution to the body force <img class="math" src="_images/math/0d2439f09c0… |
|
force applied particles in the fluid cell is:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/c24e3d875b09e3973624f97802672222ca57c3be.png" alt="\… |
|
-</div><p>where <img class="math" src="_images/math/4d3f01b8ca8bdab3543eda695ff… |
|
+<p><img src="_images/math/4eefba7b01497c1c37254ba0938852a69ca402da.png" alt="\… |
|
+</div><p>where <img class="math" src="_images/math/0e157574dc52c16b7aad0f26083… |
|
interaction force could be expanded to include the force induced by the fluid |
|
pressure gradient:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/f8484aaf38ecdf73f7489fe6b43dec92ae505398.png" alt="\… |
|
+<p><img src="_images/math/5fc35741bb341c4a7bac2b261074cee511b162b9.png" alt="\… |
|
-\nabla p + |
|
\frac{\bar{\boldsymbol{f}}_d}{1-\phi} |
|
\right) V_p"/></p> |
|
t@@ -336,10 +336,10 @@ pressure gradient:</p> |
|
<p>The partial differential terms in the previously described equations are fo… |
|
using finite central differences. Modifying the operator splitting methodology |
|
presented by Langtangen et al. (2002), the predicted velocity |
|
-<img class="math" src="_images/math/f5d499efbd23360f6e9229bdccf14e0951954730.p… |
|
-<img class="math" src="_images/math/5b4271afe7fc7c0ee84172e0ad19b82caf450c00.p… |
|
+<img class="math" src="_images/math/8615f3b3cbbe1dc55cb6b255dad751d458a4ed3c.p… |
|
+<img class="math" src="_images/math/ec002955bdf95ee9869878fbad4f80fc98539359.p… |
|
<div class="math"> |
|
-<p><img src="_images/math/4414da5fcbe9d66f08400308688cad041ca9dd9c.png" alt="\… |
|
+<p><img src="_images/math/3f8cfba42aa84819f05cca10369f3913e4833b5a.png" alt="\… |
|
+ \nabla \cdot (\phi v_x \boldsymbol{v}) |
|
= - \frac{1}{\rho} \frac{\Delta p}{\Delta x} |
|
+ \frac{1}{\rho} \left[ \nabla \cdot (\phi \boldsymbol{\tau}) \right]_x |
|
t@@ -355,10 +355,10 @@ presented by Langtangen et al. (2002), the predicted ve… |
|
+ \frac{1}{\rho} \left[ \nabla \cdot (\phi \boldsymbol{\tau}) \right]_x |
|
- \frac{1}{\rho} f^i_x |
|
+ \phi g_x"/></p> |
|
-</div><p>We want to isolate <img class="math" src="_images/math/eee8ed92791a9c… |
|
+</div><p>We want to isolate <img class="math" src="_images/math/154f421588a532… |
|
the new velocity.</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/609c6937a183637c7356d1ee9e2800015d73a5f4.png" alt="\… |
|
+<p><img src="_images/math/f8e4fccaabfa73731975fa62731bb79fed02f428.png" alt="\… |
|
= - \frac{1}{\rho} \frac{\Delta p}{\Delta x} |
|
+ \frac{1}{\rho} \left[ \nabla \cdot (\phi \boldsymbol{\tau}) \right]_x |
|
- \frac{1}{\rho} f^i_x |
|
t@@ -374,13 +374,13 @@ the new velocity.</p> |
|
+ \Delta t g_x |
|
- v_x \frac{\Delta \phi}{\phi} |
|
- \nabla \cdot (\phi v_x \boldsymbol{v}) \frac{\Delta t}{\phi}"/></p> |
|
-</div><p>The term <img class="math" src="_images/math/8ce03f78ed945f2ef3dac87c… |
|
-in the range <img class="math" src="_images/math/30d3be82eb9bf820400a3dc3e46e8… |
|
+</div><p>The term <img class="math" src="_images/math/410a9d0df9c135dd73b269cb… |
|
+in the range <img class="math" src="_images/math/b00c7b17d75d91818f2f906056232… |
|
values in the solution procedure (Langtangen et al. 2002). A value of 0 |
|
corresponds to <a class="reference external" href="https://en.wikipedia.org/wi… |
|
in <a class="reference external" href="http://www.ams.org/journals/mcom/1968-2… |
|
<div class="math"> |
|
-<p><img src="_images/math/7ac8e5caca3e02a9a9b6c9576ed9bd5effddb2fb.png" alt="v… |
|
+<p><img src="_images/math/30bcc3939e4e8f039a0879219ae7d4488c349831.png" alt="v… |
|
|
|
v_x^* = v_x^t |
|
- \frac{\beta}{\rho} \frac{\Delta p^t}{\Delta x} \frac{\Delta t}{\phi^t} |
|
t@@ -390,22 +390,22 @@ v_x^* = v_x^t |
|
+ \Delta t g_x |
|
- v^t_x \frac{\Delta \phi}{\phi^t} |
|
- \nabla \cdot (\phi^t v_x^t \boldsymbol{v}^t) \frac{\Delta t}{\phi^t}"/></p> |
|
-</div><p>Here, <img class="math" src="_images/math/98a432864561550105d4de621bc… |
|
-(<img class="math" src="_images/math/e6eadc1093d6e4f5a41f86b8301c0d7559d2c609.… |
|
-<img class="math" src="_images/math/e35ec9f12692dad5164f15f68fc16f969099e241.p… |
|
+</div><p>Here, <img class="math" src="_images/math/05899b70d35eb61a85aaaba3aff… |
|
+(<img class="math" src="_images/math/69274c46c55ea9c2723428b533616806381a2b5f.… |
|
+<img class="math" src="_images/math/acbab363f98c011e1a927c8ff8b4f565421f5def.p… |
|
equation:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/5a4c725fb6cd73a97b137a6ddc218bd457e95ab1.png" alt="\… |
|
+<p><img src="_images/math/4fc3cb57fe6e8e2710c92acae1dae02dfb464b2c.png" alt="\… |
|
\boldsymbol{v}^{t+\Delta t}) = 0"/></p> |
|
</div><p>The divergence of a scalar and vector can be <a class="reference exte… |
|
<div class="math"> |
|
-<p><img src="_images/math/6b14a983094b158179fe53e0a59ebe0d53891195.png" alt="\… |
|
+<p><img src="_images/math/dd69e8d47250a0448f829f2e1d42222cbda38058.png" alt="\… |
|
\boldsymbol{v}^{t+\Delta t} \cdot \nabla \phi^t |
|
+ \frac{\Delta \phi^t}{\Delta t} = 0"/></p> |
|
</div><p>The predicted velocity is corrected using the new pressure (Langtange… |
|
2002):</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/2fcd737952b690517150c61a5981d5e810d76268.png" alt="\… |
|
+<p><img src="_images/math/849751204b923a6bcea83d33614df1ce13444a71.png" alt="\… |
|
%- \frac{\Delta t}{\rho} \nabla \epsilon |
|
- \frac{\Delta t}{\rho \phi^t} \nabla \epsilon |
|
\quad \text{where} \quad |
|
t@@ -413,21 +413,21 @@ equation:</p> |
|
</div><p>The above formulation of the future velocity is put into the continui… |
|
equation:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/915ee93516c4e9e5e9df4b596291692f2b283c00.png" alt="\… |
|
+<p><img src="_images/math/ba57616deddc047e5626df1a0e2e2c4f49c4e95a.png" alt="\… |
|
\phi^t \nabla \cdot |
|
\left( \boldsymbol{v}^* - \frac{\Delta t}{\rho \phi^t} \nabla \epsilon \right) |
|
+ |
|
\left( \boldsymbol{v}^* - \frac{\Delta t}{\rho \phi^t} \nabla \epsilon \right) |
|
\cdot \nabla \phi^t + \frac{\Delta \phi^t}{\Delta t} = 0"/></p> |
|
</div><div class="math"> |
|
-<p><img src="_images/math/a1bc6e0933f817147b43d6662c901ffc0b2b4151.png" alt="\… |
|
+<p><img src="_images/math/5695b27fddc4f8e8a8d1194a6e74fd72eacc1a4d.png" alt="\… |
|
\phi^t \nabla \cdot |
|
\boldsymbol{v}^* - \frac{\Delta t}{\rho \phi^t} \phi^t \nabla^2 \epsilon |
|
+ \nabla \phi^t \cdot \boldsymbol{v}^* |
|
- \nabla \phi^t \cdot \nabla \epsilon \frac{\Delta t}{\rho \phi^t} |
|
+ \frac{\Delta \phi^t}{\Delta t} = 0"/></p> |
|
</div><div class="math"> |
|
-<p><img src="_images/math/03b863159155c1ff0a1478a3a14f9ceecb42221e.png" alt="\… |
|
+<p><img src="_images/math/bf12e075e2a1ffed21117ae6c3b5a57228a35e48.png" alt="\… |
|
\frac{\Delta t}{\rho} \nabla^2 \epsilon |
|
= \phi^t \nabla \cdot \boldsymbol{v}^* |
|
+ \nabla \phi^t \cdot \boldsymbol{v}^* |
|
t@@ -435,38 +435,38 @@ equation:</p> |
|
+ \frac{\Delta \phi^t}{\Delta t}"/></p> |
|
</div><p>The pressure difference in time becomes a <a class="reference externa… |
|
<div class="math"> |
|
-<p><img src="_images/math/49cc970cd820d4022dd996e66da2e453cf4aeeda.png" alt="\… |
|
+<p><img src="_images/math/af973ef88ea161ebaf13a396d18b9fd419b48392.png" alt="\… |
|
\nabla^2 \epsilon |
|
= \frac{\nabla \cdot \boldsymbol{v}^* \phi^t \rho}{\Delta t} |
|
+ \frac{\nabla \phi^t \cdot \boldsymbol{v}^* \rho}{\Delta t} |
|
- \frac{\nabla \phi^t \cdot \nabla \epsilon}{\phi^t} |
|
+ \frac{\Delta \phi^t \rho}{\Delta t^2}"/></p> |
|
</div><p>The right hand side of the above equation is termed the <em>forcing f… |
|
-<img class="math" src="_images/math/0001d02b63ede2fe3219e05a7cd09c82ae6298b6.p… |
|
+<img class="math" src="_images/math/875eb40014526135383caa89fd500ae40a835f56.p… |
|
<div class="math"> |
|
-<p><img src="_images/math/ba756dc27a3f5d7f8ff7d7801d8c444393c13e6a.png" alt="f… |
|
+<p><img src="_images/math/6d2f443abfc2651609cd8dd745ff62139f7d51c4.png" alt="f… |
|
= \frac{\nabla \cdot \boldsymbol{v}^* \phi^t \rho}{\Delta t} |
|
+ \frac{\nabla \phi^t \cdot \boldsymbol{v}^* \rho}{\Delta t} |
|
+ \frac{\Delta \phi^t \rho}{\Delta t^2} |
|
|
|
f_2 = |
|
\frac{\nabla \phi^t \cdot \nabla \epsilon}{\phi^t}"/></p> |
|
-</div><p>During the <a class="reference external" href="http://www.rsmas.miami… |
|
-while <img class="math" src="_images/math/ff9078c258266635e46b9767b0c7e248c865… |
|
-during the first iteration, while <img class="math" src="_images/math/ff9078c2… |
|
+</div><p>During the <a class="reference external" href="http://www.rsmas.miami… |
|
+while <img class="math" src="_images/math/a23addf1349384bc83f74ce7c550fe98bbdc… |
|
+during the first iteration, while <img class="math" src="_images/math/a23addf1… |
|
of the forcing function is found as:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/2a6ab5768c27f4033a07a2bd556e89a39cdff6c0.png" alt="f… |
|
+<p><img src="_images/math/7145387c0de7584800cc45b61520c507b70038cb.png" alt="f… |
|
</div><p>Using second-order finite difference approximations of the Laplace op… |
|
second-order partial derivatives, the differential equations become a system of |
|
equations that is solved using <a class="reference external" href="https://en.… |
|
-number of unknowns is <img class="math" src="_images/math/7774004c6a3397305cc7… |
|
+number of unknowns is <img class="math" src="_images/math/046284126cf107c26a29… |
|
<p>The discrete Laplacian (approximation of the Laplace operator) can be obtai… |
|
by a finite-difference seven-point stencil in a three-dimensional, cubic |
|
-grid with cell spacing <img class="math" src="_images/math/43e42baf6cef7e96200… |
|
+grid with cell spacing <img class="math" src="_images/math/fffb1eace0724fc01f1… |
|
face neighbors:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/ae70bc18ed864da95e96ab31ccce2f21f06d6979.png" alt="\… |
|
+<p><img src="_images/math/976d1f7bdf9faa8c8c428dbcc25b1540eedaa139.png" alt="\… |
|
\frac{\epsilon_{i_x-1,i_y,i_z} - 2 \epsilon_{i_x,i_y,i_z} |
|
+ \epsilon_{i_x+1,i_y,i_z}}{\Delta x^2} |
|
+ \frac{\epsilon_{i_x,i_y-1,i_z} - 2 \epsilon_{i_x,i_y,i_z} |
|
t@@ -475,11 +475,11 @@ face neighbors:</p> |
|
+ \frac{\epsilon_{i_x,i_y,i_z-1} - 2 \epsilon_{i_x,i_y,i_z} |
|
+ \epsilon_{i_x,i_y,i_z+1}}{\Delta z^2} |
|
\approx f_{i_x,i_y,i_z}"/></p> |
|
-</div><p>Within a Jacobi iteration, the value of the unknowns (<img class="mat… |
|
-used to find an updated solution estimate (<img class="math" src="_images/math… |
|
+</div><p>Within a Jacobi iteration, the value of the unknowns (<img class="mat… |
|
+used to find an updated solution estimate (<img class="math" src="_images/math… |
|
The solution for the updated value takes the form:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/11c52ddf6d9f9157b67c1334ccb39807a8ee777c.png" alt="\… |
|
+<p><img src="_images/math/52f1699b7bdfcd7da418c1f5639cfdfa40ed99a7.png" alt="\… |
|
= \frac{-\Delta x^2 \Delta y^2 \Delta z^2 f_{i_x,i_y,i_z} |
|
+ \Delta y^2 \Delta z^2 (\epsilon^n_{i_x-1,i_y,i_z} + |
|
\epsilon^n_{i_x+1,i_y,i_z}) |
|
t@@ -493,42 +493,42 @@ The solution for the updated value takes the form:</p> |
|
</div><p>The difference between the current and updated value is termed the <e… |
|
residual</em>:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/a6f6238418bca503a9616e884c92c10d86d34fbc.png" alt="r… |
|
+<p><img src="_images/math/b843ab93a9cd31bd2f99132fe09390b3b2e69b96.png" alt="r… |
|
- \epsilon^n_{i_x,i_y,i_z})^2}{(\epsilon^{n+1}_{i_x,i_y,i_z})^2}"/></p> |
|
-</div><p>Note that the <img class="math" src="_images/math/19bc0073dde1bcd1a8e… |
|
+</div><p>Note that the <img class="math" src="_images/math/65d19c66c148d5016c6… |
|
of the residual.</p> |
|
<p>The updated values are at the end of the iteration stored as the current va… |
|
and the maximal value of the normalized residual is found. If this value is |
|
larger than a tolerance criteria, the procedure is repeated. The iterative |
|
procedure is ended if the number of iterations exceeds a defined limit.</p> |
|
-<p>After the values of <img class="math" src="_images/math/19bc0073dde1bcd1a8e… |
|
+<p>After the values of <img class="math" src="_images/math/65d19c66c148d5016c6… |
|
pressures and velocities:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/e80afabbf8aabeec85a867c9c73d1f2df69743fa.png" alt="\… |
|
+<p><img src="_images/math/34ae3abc95078f1fbc7d24815a091daacc0293d6.png" alt="\… |
|
</div><div class="math"> |
|
-<p><img src="_images/math/26446b608e4ea66bd2ac56325be3b7dad3ec4261.png" alt="\… |
|
+<p><img src="_images/math/d653d13e7a5e33414bfff96b3015fb597c5355f5.png" alt="\… |
|
\bar{\boldsymbol{v}}^* - \frac{\Delta t}{\rho\phi} \nabla \epsilon"/></p> |
|
</div></div> |
|
<div class="section" id="boundary-conditions"> |
|
<h2>Boundary conditions<a class="headerlink" href="#boundary-conditions" title… |
|
<p>The lateral boundaries are periodic. This cannot be changed in the current |
|
version of <code class="docutils literal"><span class="pre">sphere</span></cod… |
|
-parallel lateral (<img class="math" src="_images/math/188c175aac0a8a9c22499336… |
|
+parallel lateral (<img class="math" src="_images/math/a59f68a4202623bb859a7093… |
|
leaving through one side reappears on the opposite side.</p> |
|
<p>The top and bottom boundary conditions of the fluid grid can be either: |
|
prescribed pressure (Dirichlet), or prescribed velocity (Neumann). The |
|
(horizontal) velocities parallel to the boundaries are free to attain other |
|
values (free slip). The Dirichlet boundary condition is enforced by keeping the |
|
-value of <img class="math" src="_images/math/19bc0073dde1bcd1a8e6a32b251e80cce… |
|
+value of <img class="math" src="_images/math/65d19c66c148d5016c6a89d26486bf6d1… |
|
<div class="math"> |
|
-<p><img src="_images/math/d04d640e7e6ee0fbcd4ba0e9fc6cb43f3e536d12.png" alt="\… |
|
+<p><img src="_images/math/9b35bf83c6ef9ec4ea134990256960d8e1c204d0.png" alt="\… |
|
= |
|
\epsilon^{n}_{i_x,i_y,i_z = 1 \vee n_z}"/></p> |
|
</div><p>The Neumann boundary condition of no flow across the boundary is enfo… |
|
-setting the gradient of <img class="math" src="_images/math/19bc0073dde1bcd1a8… |
|
+setting the gradient of <img class="math" src="_images/math/65d19c66c148d5016c… |
|
e.g.:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/f82d0eba51cfeff3da50b567ffa5126a8ed5b15f.png" alt="\… |
|
+<p><img src="_images/math/e244cc08185d93b146a75a8fa9618b0c83b80db3.png" alt="\… |
|
</div></div> |
|
<div class="section" id="numerical-implementation"> |
|
<h2>Numerical implementation<a class="headerlink" href="#numerical-implementat… |
|
t@@ -598,7 +598,7 @@ e.g.:</p> |
|
<li class="right" > |
|
<a href="dem.html" title="Discrete element method" |
|
>previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
<div class="footer" role="contentinfo"> |
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
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- <title>Discrete element method — sphere 1.00-alpha documentation</ti… |
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+ <title>Discrete element method — sphere 2.15-beta documentation</tit… |
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URL_ROOT: './', |
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+ VERSION: '2.15-beta', |
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FILE_SUFFIX: '.html', |
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t@@ -25,7 +25,7 @@ |
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<script type="text/javascript" src="_static/doctools.js"></script> |
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<li class="right" > |
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<a href="introduction.html" title="Introduction and Installation" |
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accesskey="P">previous</a> |</li> |
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- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
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+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
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t@@ -82,10 +82,10 @@ derivative.</p> |
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<h2>Contact search<a class="headerlink" href="#contact-search" title="Permalin… |
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<p>Homogeneous cubic grid.</p> |
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<div class="math"> |
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-<p><img src="_images/math/7a1586ce67a2a8d709a374bb524625ca12559fd0.png" alt="\… |
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-</div><p>where <img class="math" src="_images/math/2ede365ad144ab396916ec60458… |
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-positional vector of a particle, and <img class="math" src="_images/math/a581f… |
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-of two particles. Negative values of <img class="math" src="_images/math/2822d… |
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+<p><img src="_images/math/9a32e316af25b770f61240f0c87520e61a20170e.png" alt="\… |
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+</div><p>where <img class="math" src="_images/math/eaa6ad49a7f78fe5a13b4866901… |
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+positional vector of a particle, and <img class="math" src="_images/math/df0de… |
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+of two particles. Negative values of <img class="math" src="_images/math/f20d5… |
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are overlapping.</p> |
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</div> |
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<div class="section" id="contact-interaction"> |
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t@@ -96,12 +96,12 @@ interaction is decomposed into normal and tangential compo… |
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contact interface orientation. The normal vector to the contact interface is |
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found by:</p> |
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<div class="math"> |
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-<p><img src="_images/math/b2f647d3f64c336d2581f03558393e1dbb92c919.png" alt="\… |
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+<p><img src="_images/math/edf49df0f6a5c2f2624ad844873e377c86bd3e50.png" alt="\… |
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\frac{\boldsymbol{x}^i - \boldsymbol{x}^j} |
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{||\boldsymbol{x}^i - \boldsymbol{x}^j||}"/></p> |
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-</div><p>The contact velocity <img class="math" src="_images/math/522c9c96bc63… |
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+</div><p>The contact velocity <img class="math" src="_images/math/18c042632208… |
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<div class="math"> |
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-<p><img src="_images/math/3e0f4950bf4cf691a83dd643eddd240f024b9806.png" alt="\… |
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+<p><img src="_images/math/dc9ba965d2e46bab75a9783346180b4e90516118.png" alt="\… |
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(\boldsymbol{x}^i - \boldsymbol{x}^j) |
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+ (r^i + \frac{\delta_n^{ij}}{2}) |
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(\boldsymbol{n}^{ij} \times \boldsymbol{\omega}^{i}) |
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t@@ -110,28 +110,28 @@ found by:</p> |
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</div><p>The contact velocity is decomposed into normal and tangential compone… |
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relative to the contact interface. The normal component is:</p> |
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<div class="math"> |
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-<p><img src="_images/math/d5f7df718c75314abef3cc68396ac19229c2b55d.png" alt="\… |
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+<p><img src="_images/math/7064634d7b87e0dd07b7dcfee5d1ab549b5964fa.png" alt="\… |
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-(\dot{\boldsymbol{\delta}}^{ij} \cdot \boldsymbol{n}^{ij})"/></p> |
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</div><p>and the tangential velocity component is found as:</p> |
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<div class="math"> |
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-<p><img src="_images/math/10eaed38fefc0732b59e674c14396ff74ea89c93.png" alt="\… |
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+<p><img src="_images/math/e9905af08d85a280a4c2996689972016f7833fef.png" alt="\… |
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\dot{\boldsymbol{\delta}}^{ij} |
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- \boldsymbol{n}^{ij} |
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(\boldsymbol{n}^{ij} \cdot \dot{\boldsymbol{\delta}}^{ij})"/></p> |
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-</div><p>where <img class="math" src="_images/math/b95363838d60e863c4cb530ba40… |
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+</div><p>where <img class="math" src="_images/math/cd1d64597c760ff1fc8d90d0d08… |
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particle. The total tangential displacement on the contact plane is found |
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incrementally:</p> |
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<div class="math"> |
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-<p><img src="_images/math/904bfd360afed4f050929e89e2cc4f7c6f673e97.png" alt="\… |
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+<p><img src="_images/math/d3e56488ee50f821a999470459f170e3b0cac3d3.png" alt="\… |
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\int_0^{t_c} |
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\dot{\boldsymbol{\delta}}^{ij}_t \Delta t"/></p> |
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-</div><p>where <img class="math" src="_images/math/42ea00932c36940fb8965e6e7f4… |
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+</div><p>where <img class="math" src="_images/math/b8cd14d20ff38e8c9e305878c37… |
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computational time step length. The tangential contact interface displacement … |
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set to zero when a contact pair no longer overlaps. At each time step, the val… |
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-of <img class="math" src="_images/math/8cfa62046b3a57f37068f027941acea702d9bd8… |
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+of <img class="math" src="_images/math/359991b87d5889ece1cd8b1c84cf17fbb37b815… |
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interface:</p> |
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<div class="math"> |
|
-<p><img src="_images/math/ef61e2c4dfb9fcb1053c8d2557e00bcf3d871b80.png" alt="\… |
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+<p><img src="_images/math/71b3ac73bf6447e6cc7ea151b5664dc723a38ea9.png" alt="\… |
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- (\boldsymbol{n} |
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(\boldsymbol{n} \cdot \boldsymbol{\delta}_{t,\text{uncorrected}}^{ij})"/></p> |
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</div><p>With all the geometrical and kinetic components determined, the resul… |
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t@@ -139,17 +139,17 @@ of the particle interaction can be determined using a co… |
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features only one contact model in the normal direction to the contact; the |
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linear-elastic-viscous (<em>Hookean</em> with viscous damping, or <em>Kelvin-V… |
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contact model. The resulting force in the normal direction of the contact |
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-interface on particle <img class="math" src="_images/math/a581f053bbfa5115f42c… |
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+interface on particle <img class="math" src="_images/math/df0deb143e5ac127f00b… |
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<div class="math"> |
|
-<p><img src="_images/math/7d72e011d7f06b5df7ff7decf324f701eae33c3a.png" alt="\… |
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+<p><img src="_images/math/2b331ff6c55b9e20fb12706828da440a9ef5b20c.png" alt="\… |
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-k_n \delta_n^{ij} -\gamma_n \dot{\delta_n}^{ij} |
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\right) \boldsymbol{n}^{ij}"/></p> |
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-</div><p>The parameter <img class="math" src="_images/math/66a1d8738af51528641… |
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-contact interface, and <img class="math" src="_images/math/3640b174f15a44d33ad… |
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+</div><p>The parameter <img class="math" src="_images/math/e8082d4f9b7dfa49370… |
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+contact interface, and <img class="math" src="_images/math/ae2c9cf2d489e787ac1… |
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viscosity, also in the normal direction. The loss of energy in this interaction |
|
-due to the viscous component is for particle <img class="math" src="_images/ma… |
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+due to the viscous component is for particle <img class="math" src="_images/ma… |
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<div class="math"> |
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-<p><img src="_images/math/4305b4408a39583be7a127c3039d65ff0cd8c954.png" alt="\… |
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+<p><img src="_images/math/89eab38386c7248f117087bc9f112b43b2a60010.png" alt="\… |
|
</div><p>The tangential force is determined by either a viscous-frictional con… |
|
or a elastic-viscous-frictional contact model. The former contact model is very |
|
computationally efficient, but somewhat inaccurate relative to the mechanics of |
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t@@ -157,24 +157,24 @@ real materials. The latter contact model is therefore t… |
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it results in longer computational times. The tangential force in the |
|
visco-frictional contact model:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/f808e880e30ba99dc461a8dfdaaca903e8433bc1.png" alt="\… |
|
-</div><p><img class="math" src="_images/math/3640b174f15a44d33ad8f0622bc44dce8… |
|
+<p><img src="_images/math/6fa02b1c3bc8a438f685b666895f7de1f427b702.png" alt="\… |
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+</div><p><img class="math" src="_images/math/ae2c9cf2d489e787ac1340cc4436f6100… |
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direction. The tangential displacement along the contact interface |
|
-(<img class="math" src="_images/math/8cfa62046b3a57f37068f027941acea702d9bd8a.… |
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+(<img class="math" src="_images/math/359991b87d5889ece1cd8b1c84cf17fbb37b815d.… |
|
model. The tangential force in the more realistic elastic-viscous-frictional |
|
contact model:</p> |
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<div class="math"> |
|
-<p><img src="_images/math/e3d643e0cb551cafec2614062e50e2369d7949ab.png" alt="\… |
|
+<p><img src="_images/math/365556da97364e0ebe011deb8a6114cc57208b69.png" alt="\… |
|
-k_t \boldsymbol{\delta}_t^{ij} -\gamma_t \dot{\boldsymbol{\delta}_t}^{ij}"/><… |
|
-</div><p>The parameter <img class="math" src="_images/math/66a1d8738af51528641… |
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+</div><p>The parameter <img class="math" src="_images/math/e8082d4f9b7dfa49370… |
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direction of the contact interface. Note that the tangential force is only |
|
-found if the tangential displacement (<img class="math" src="_images/math/d18b… |
|
-velocity (<img class="math" src="_images/math/6b038d0d06f6fa38bcb85df9e6f8bed4… |
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-zero. Otherwise it is defined as being <img class="math" src="_images/math/b3c… |
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+found if the tangential displacement (<img class="math" src="_images/math/1820… |
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+velocity (<img class="math" src="_images/math/3f1d577c0a6a09ed5b13001794297b2b… |
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+zero. Otherwise it is defined as being <img class="math" src="_images/math/6a4… |
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<p>For both types of contact model, the tangential force is limited by the Cou… |
|
criterion of static and dynamic friction:</p> |
|
<div class="math"> |
|
-<p><img src="_images/math/5cc160009025ab2cd3b77343dcea454fb8c93795.png" alt="|… |
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+<p><img src="_images/math/edcde9b8cbb2394c6bbd12f07b845063be99a62e.png" alt="|… |
|
\begin{cases} |
|
\mu_s ||\boldsymbol{f}^{ij}_n|| & |
|
\text{if} \quad ||\boldsymbol{f}_t^{ij}|| = 0 \\ |
|
t@@ -185,7 +185,7 @@ criterion of static and dynamic friction:</p> |
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reached, the tangential displacement along the contact interface is limited to |
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this value:</p> |
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<div class="math"> |
|
-<p><img src="_images/math/13ac3fb2c8f5e95101d362b1cb57b5fcb70e9a71.png" alt="\… |
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+<p><img src="_images/math/092547c763f745333b005b7094cd03c2cfdd92f5.png" alt="\… |
|
\frac{1}{k_t} \left( |
|
\mu_d ||\boldsymbol{f}_n^{ij}|| |
|
\frac{\boldsymbol{f}^{ij}_t}{||\boldsymbol{f}^{ij}_t||} |
|
t@@ -193,30 +193,30 @@ this value:</p> |
|
</div><p>If the tangential force reaches the Coulomb limit, the energy lost du… |
|
frictional dissipation is calculated as:</p> |
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<div class="math"> |
|
-<p><img src="_images/math/85bd2d6544d7812f80cc49d2b7e94be81541301c.png" alt="\… |
|
+<p><img src="_images/math/a699d5b66f6ff1048229d376ae6340ce0ed5ed6b.png" alt="\… |
|
\dot{\boldsymbol{\delta}}_t^{ij} \Delta t||}{\Delta t}"/></p> |
|
</div><p>The loss of energy by viscous dissipation in the tangential direction… |
|
found.</p> |
|
</div> |
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<div class="section" id="temporal-integration"> |
|
<h2>Temporal integration<a class="headerlink" href="#temporal-integration" tit… |
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-<p>In the DEM, the time is discretized into small steps (<img class="math" src… |
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+<p>In the DEM, the time is discretized into small steps (<img class="math" src… |
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step, the entire network of contacts is resolved, and the resulting forces and |
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torques for each particle are found. With these values at hand, the new |
|
linear and rotational accelerations can be found using |
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<a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_l… |
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-of the motion of solid bodies. If a particle with mass <img class="math" src="… |
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-experiences a sum of forces denoted <img class="math" src="_images/math/8f28ce… |
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-(<img class="math" src="_images/math/701df29c5482cdf1e577052c537c176f5a12caf5.… |
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+of the motion of solid bodies. If a particle with mass <img class="math" src="… |
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+experiences a sum of forces denoted <img class="math" src="_images/math/e5861e… |
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+(<img class="math" src="_images/math/1a238040fa47ba4651506e01c721eb94a03f11ba.… |
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<div class="math"> |
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-<p><img src="_images/math/5bab09e6e7765565f55e2f7119251f199f472a4a.png" alt="\… |
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+<p><img src="_images/math/7a16f81eae500f9872de54d88258152bfb0ccbc6.png" alt="\… |
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</div><p>The new velocity and position is found by integrating the above equat… |
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with regards to time. The simplest integration scheme in this regard is the |
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<a class="reference external" href="https://en.wikipedia.org/wiki/Euler_method… |
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<div class="math"> |
|
-<p><img src="_images/math/a038fb9a65b9138665b4a5c9d0bbba6bdf3b6dbc.png" alt="\… |
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+<p><img src="_images/math/3d4d7c98c0c7511ac5480967994253f526e13af6.png" alt="\… |
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</div><div class="math"> |
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-<p><img src="_images/math/ef4b452d768af650e6ddc2fd95aff430284f74f2.png" alt="\… |
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+<p><img src="_images/math/91bab0359c2bff8094d2fed7299dc2ca80a27d74.png" alt="\… |
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</div></div> |
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</div> |
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|
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t@@ -278,7 +278,7 @@ with regards to time. The simplest integration scheme in t… |
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- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
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diff --git a/doc/html/genindex.html b/doc/html/genindex.html |
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t@@ -7,7 +7,7 @@ |
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
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- <title>Index — sphere 1.00-alpha documentation</title> |
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+ <title>Index — sphere 2.15-beta documentation</title> |
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URL_ROOT: './', |
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t@@ -26,7 +26,7 @@ |
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t@@ -38,7 +38,7 @@ |
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t@@ -6,7 +6,7 @@ |
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
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<script type="text/javascript"> |
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var DOCUMENTATION_OPTIONS = { |
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URL_ROOT: './', |
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+ VERSION: '2.15-beta', |
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FILE_SUFFIX: '.html', |
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HAS_SOURCE: true |
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t@@ -25,7 +25,7 @@ |
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<script type="text/javascript" src="_static/doctools.js"></script> |
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<link rel="index" title="Index" href="genindex.html" /> |
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<link rel="search" title="Search" href="search.html" /> |
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+ <link rel="top" title="sphere 2.15-beta documentation" href="#" /> |
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accesskey="N">next</a> |</li> |
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t@@ -161,7 +161,7 @@ party developers. This document is a work in progress.</p> |
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>next</a> |</li> |
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diff --git a/doc/html/introduction.html b/doc/html/introduction.html |
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t@@ -6,7 +6,7 @@ |
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<li class="right" > |
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<a href="index.html" title="The sphere documentation" |
|
accesskey="P">previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
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|
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t@@ -185,9 +185,11 @@ from the root directory:</p> |
|
<div class="highlight-default"><div class="highlight"><pre><span></span>$ cmak… |
|
</pre></div> |
|
</div> |
|
-<p>NOTE: If your system does not have a GCC compiler (e.g. GCC-5 for CUDA 8) |
|
-compatible with the installed CUDA version, try using <code class="docutils li… |
|
-<div class="highlight-default"><div class="highlight"><pre><span></span>$ expo… |
|
+<p>NOTE: If your system does not have a GCC compiler compatible with the insta… |
|
+CUDA version (e.g. GCC-5 for CUDA 8), you will see errors at the linker stage. |
|
+In that case, try using <code class="docutils literal"><span class="pre">clang… |
|
+<div class="highlight-default"><div class="highlight"><pre><span></span>$ rm -… |
|
+$ export CC=$(which clang-3.8) && export CXX=$(which clang++-3.8) &… |
|
</pre></div> |
|
</div> |
|
<p>After a successfull installation, the <code class="docutils literal"><span … |
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t@@ -216,13 +218,9 @@ following commands to check the executable:</p> |
|
| | | | |
|
| |_| Version: 2.15 | |
|
`-------------------------------------ยด |
|
- A discrete element method particle dynamics simulator. |
|
+ A discrete-element method particle dynamics simulator. |
|
Written by Anders Damsgaard, license GPLv3+. |
|
- https://cs.au.dk/~adc/ |
|
-</pre></div> |
|
-</div> |
|
-<p>The build can be verified by running a number of automated tests:</p> |
|
-<div class="highlight-default"><div class="highlight"><pre><span></span>$ make… |
|
+ https://adamsgaard.dk |
|
</pre></div> |
|
</div> |
|
<p>The documentation can be read in the <a class="reference external" href="ht… |
|
t@@ -254,7 +252,7 @@ a simulation is typically arranged in the following order:… |
|
<blockquote> |
|
<div><ul class="simple"> |
|
<li>Setup of particle assemblage, physical properties and conditions using the |
|
-Python API.</li> |
|
+Python API (<code class="docutils literal"><span class="pre">python/sphere.py<… |
|
<li>Execution of <code class="docutils literal"><span class="pre">sphere</span… |
|
function of time, as a result of the conditions initially specified in the |
|
input file.</li> |
|
t@@ -325,7 +323,7 @@ in Python, and/or scene rendering using the built-in ray t… |
|
<li class="right" > |
|
<a href="index.html" title="The sphere documentation" |
|
>previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
<div class="footer" role="contentinfo"> |
|
diff --git a/doc/html/objects.inv b/doc/html/objects.inv |
|
Binary files differ. |
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diff --git a/doc/html/py-modindex.html b/doc/html/py-modindex.html |
|
t@@ -6,7 +6,7 @@ |
|
<head> |
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
|
|
|
- <title>Python Module Index — sphere 1.00-alpha documentation</title> |
|
+ <title>Python Module Index — sphere 2.15-beta documentation</title> |
|
|
|
<link rel="stylesheet" href="_static/classic.css" type="text/css" /> |
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<link rel="stylesheet" href="_static/pygments.css" type="text/css" /> |
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t@@ -14,7 +14,7 @@ |
|
<script type="text/javascript"> |
|
var DOCUMENTATION_OPTIONS = { |
|
URL_ROOT: './', |
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- VERSION: '1.00-alpha', |
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+ VERSION: '2.15-beta', |
|
COLLAPSE_INDEX: false, |
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FILE_SUFFIX: '.html', |
|
HAS_SOURCE: true |
|
t@@ -25,7 +25,7 @@ |
|
<script type="text/javascript" src="_static/doctools.js"></script> |
|
<link rel="index" title="Index" href="genindex.html" /> |
|
<link rel="search" title="Search" href="search.html" /> |
|
- <link rel="top" title="sphere 1.00-alpha documentation" href="index.html" … |
|
+ <link rel="top" title="sphere 2.15-beta documentation" href="index.html" /> |
|
|
|
|
|
<script type="text/javascript"> |
|
t@@ -44,7 +44,7 @@ |
|
<li class="right" > |
|
<a href="#" title="Python Module Index" |
|
>modules</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
|
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t@@ -100,7 +100,7 @@ |
|
<li class="right" > |
|
<a href="#" title="Python Module Index" |
|
>modules</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
<div class="footer" role="contentinfo"> |
|
diff --git a/doc/html/python_api.html b/doc/html/python_api.html |
|
t@@ -6,7 +6,7 @@ |
|
<head> |
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
|
|
|
- <title>Python API — sphere 1.00-alpha documentation</title> |
|
+ <title>Python API — sphere 2.15-beta documentation</title> |
|
|
|
<link rel="stylesheet" href="_static/classic.css" type="text/css" /> |
|
<link rel="stylesheet" href="_static/pygments.css" type="text/css" /> |
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t@@ -14,7 +14,7 @@ |
|
<script type="text/javascript"> |
|
var DOCUMENTATION_OPTIONS = { |
|
URL_ROOT: './', |
|
- VERSION: '1.00-alpha', |
|
+ VERSION: '2.15-beta', |
|
COLLAPSE_INDEX: false, |
|
FILE_SUFFIX: '.html', |
|
HAS_SOURCE: true |
|
t@@ -25,7 +25,8 @@ |
|
<script type="text/javascript" src="_static/doctools.js"></script> |
|
<link rel="index" title="Index" href="genindex.html" /> |
|
<link rel="search" title="Search" href="search.html" /> |
|
- <link rel="top" title="sphere 1.00-alpha documentation" href="index.html" … |
|
+ <link rel="top" title="sphere 2.15-beta documentation" href="index.html" /> |
|
+ <link rel="next" title="sphere internals" href="sphere_internals.html" /> |
|
<link rel="prev" title="Fluid simulation and particle-fluid interaction" h… |
|
</head> |
|
<body role="document"> |
|
t@@ -39,9 +40,12 @@ |
|
<a href="py-modindex.html" title="Python Module Index" |
|
>modules</a> |</li> |
|
<li class="right" > |
|
+ <a href="sphere_internals.html" title="sphere internals" |
|
+ accesskey="N">next</a> |</li> |
|
+ <li class="right" > |
|
<a href="cfd.html" title="Fluid simulation and particle-fluid intera… |
|
accesskey="P">previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
|
|
t@@ -1154,7 +1158,7 @@ parameter <cite>hydrostatic</cite> is set to <cite>True<… |
|
the fluid cells at the top</li> |
|
<li><strong>hydrostatic</strong> (<em>bool</em>) – Initialize the fluid … |
|
pressure distribution. A pressure gradient with depth is only |
|
-created if a gravitational acceleration along <img class="math" src="_images/m… |
|
+created if a gravitational acceleration along <img class="math" src="_images/m… |
|
has been specified</li> |
|
<li><strong>cfd_solver</strong> (<em>int</em>) – Solver to use for the c… |
|
Accepted values: 0 (Navier Stokes, default) and 1 (Darcy).</li> |
|
t@@ -3376,6 +3380,9 @@ rendered beforehand using <a class="reference internal" … |
|
<h4>Previous topic</h4> |
|
<p class="topless"><a href="cfd.html" |
|
title="previous chapter">Fluid simulation and particle… |
|
+ <h4>Next topic</h4> |
|
+ <p class="topless"><a href="sphere_internals.html" |
|
+ title="next chapter">sphere internals</a></p> |
|
<div role="note" aria-label="source link"> |
|
<h3>This Page</h3> |
|
<ul class="this-page-menu"> |
|
t@@ -3407,9 +3414,12 @@ rendered beforehand using <a class="reference internal"… |
|
<a href="py-modindex.html" title="Python Module Index" |
|
>modules</a> |</li> |
|
<li class="right" > |
|
+ <a href="sphere_internals.html" title="sphere internals" |
|
+ >next</a> |</li> |
|
+ <li class="right" > |
|
<a href="cfd.html" title="Fluid simulation and particle-fluid intera… |
|
>previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
<div class="footer" role="contentinfo"> |
|
diff --git a/doc/html/search.html b/doc/html/search.html |
|
t@@ -6,7 +6,7 @@ |
|
<head> |
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
|
|
|
- <title>Search — sphere 1.00-alpha documentation</title> |
|
+ <title>Search — sphere 2.15-beta documentation</title> |
|
|
|
<link rel="stylesheet" href="_static/classic.css" type="text/css" /> |
|
<link rel="stylesheet" href="_static/pygments.css" type="text/css" /> |
|
t@@ -14,7 +14,7 @@ |
|
<script type="text/javascript"> |
|
var DOCUMENTATION_OPTIONS = { |
|
URL_ROOT: './', |
|
- VERSION: '1.00-alpha', |
|
+ VERSION: '2.15-beta', |
|
COLLAPSE_INDEX: false, |
|
FILE_SUFFIX: '.html', |
|
HAS_SOURCE: true |
|
t@@ -26,7 +26,7 @@ |
|
<script type="text/javascript" src="_static/searchtools.js"></script> |
|
<link rel="index" title="Index" href="genindex.html" /> |
|
<link rel="search" title="Search" href="#" /> |
|
- <link rel="top" title="sphere 1.00-alpha documentation" href="index.html" … |
|
+ <link rel="top" title="sphere 2.15-beta documentation" href="index.html" /> |
|
<script type="text/javascript"> |
|
jQuery(function() { Search.loadIndex("searchindex.js"); }); |
|
</script> |
|
t@@ -45,7 +45,7 @@ |
|
<li class="right" > |
|
<a href="py-modindex.html" title="Python Module Index" |
|
>modules</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
|
|
t@@ -96,7 +96,7 @@ |
|
<li class="right" > |
|
<a href="py-modindex.html" title="Python Module Index" |
|
>modules</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
<div class="footer" role="contentinfo"> |
|
diff --git a/doc/html/searchindex.js b/doc/html/searchindex.js |
|
t@@ -1 +1 @@ |
|
-Search.setIndex({envversion:49,filenames:["cfd","dem","index","introduction","… |
|
-\ No newline at end of file |
|
+Search.setIndex({envversion:49,filenames:["cfd","dem","index","introduction","… |
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+\ No newline at end of file |
|
diff --git a/doc/html/sphere_internals.html b/doc/html/sphere_internals.html |
|
t@@ -6,7 +6,7 @@ |
|
<head> |
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
|
|
|
- <title>sphere internals — sphere 1.00-alpha documentation</title> |
|
+ <title>sphere internals — sphere 2.15-beta documentation</title> |
|
|
|
<link rel="stylesheet" href="_static/classic.css" type="text/css" /> |
|
<link rel="stylesheet" href="_static/pygments.css" type="text/css" /> |
|
t@@ -14,7 +14,7 @@ |
|
<script type="text/javascript"> |
|
var DOCUMENTATION_OPTIONS = { |
|
URL_ROOT: './', |
|
- VERSION: '1.00-alpha', |
|
+ VERSION: '2.15-beta', |
|
COLLAPSE_INDEX: false, |
|
FILE_SUFFIX: '.html', |
|
HAS_SOURCE: true |
|
t@@ -25,7 +25,7 @@ |
|
<script type="text/javascript" src="_static/doctools.js"></script> |
|
<link rel="index" title="Index" href="genindex.html" /> |
|
<link rel="search" title="Search" href="search.html" /> |
|
- <link rel="top" title="sphere 1.00-alpha documentation" href="index.html" … |
|
+ <link rel="top" title="sphere 2.15-beta documentation" href="index.html" /> |
|
<link rel="prev" title="Python API" href="python_api.html" /> |
|
</head> |
|
<body role="document"> |
|
t@@ -41,7 +41,7 @@ |
|
<li class="right" > |
|
<a href="python_api.html" title="Python API" |
|
accesskey="P">previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
|
|
t@@ -217,8 +217,8 @@ item Update of verb”<simulation_ID>.status#..b… |
|
</ol> |
|
<p>The length of the computational time steps (texttt{time.dt}) is calculated … |
|
<div class="math"> |
|
-<p><img src="_images/math/6af8f3510a4e3f1aea74c1b180c9d93ef248128c.png" alt="\… |
|
-</div><p>where <img class="math" src="_images/math/c4bb40dd65eae6c11b325989b14… |
|
+<p><img src="_images/math/f068b70724ff65c62363e69535c2b276fab6dad3.png" alt="\… |
|
+</div><p>where <img class="math" src="_images/math/edba97b4c0d864d26e92ea7ea73… |
|
The time step is set by this relationship in <code class="xref py py-func docu… |
|
This equation ensures that the elastic wave (traveling at the speed of sound) … |
|
<p>subsubsection{Host and device memory types} |
|
t@@ -302,7 +302,7 @@ An important note is that the texttt{C} examples of the NV… |
|
<li class="right" > |
|
<a href="python_api.html" title="Python API" |
|
>previous</a> |</li> |
|
- <li class="nav-item nav-item-0"><a href="index.html">sphere 1.00-alpha… |
|
+ <li class="nav-item nav-item-0"><a href="index.html">sphere 2.15-beta … |
|
</ul> |
|
</div> |
|
<div class="footer" role="contentinfo"> |
|
diff --git a/doc/pdf/sphere.pdf b/doc/pdf/sphere.pdf |
|
Binary files differ. |
|
diff --git a/doc/sphinx/conf.py b/doc/sphinx/conf.py |
|
t@@ -32,7 +32,10 @@ sys.path.insert(0, os.path.abspath('../../python/')) |
|
# Add any Sphinx extension module names here, as strings. They can be extensio… |
|
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones. |
|
#extensions = [] |
|
-extensions = ['sphinx.ext.autodoc','breathe','sphinx.ext.pngmath','sphinxcontr… |
|
+extensions = ['sphinx.ext.autodoc', |
|
+ 'breathe', |
|
+ 'sphinx.ext.imgmath', |
|
+ 'sphinxcontrib.programoutput'] |
|
breathe_projects = { "sphere": "../doxygen/xml/" } |
|
breathe_default_project = "sphere" |
|
|
|
t@@ -57,9 +60,9 @@ copyright = u'2014, Anders Damsgaard' |
|
# built documents. |
|
# |
|
# The short X.Y version. |
|
-version = '1.00' |
|
+version = '2.15' |
|
# The full version, including alpha/beta/rc tags. |
|
-release = '1.00-alpha' |
|
+release = '2.15-beta' |
|
|
|
# The language for content autogenerated by Sphinx. Refer to documentation |
|
# for a list of supported languages. |
|
diff --git a/doc/sphinx/introduction.rst b/doc/sphinx/introduction.rst |
|
t@@ -132,9 +132,11 @@ from the root directory:: |
|
|
|
$ cmake . && make |
|
|
|
-NOTE: If your system does not have a GCC compiler (e.g. GCC-5 for CUDA 8) |
|
-compatible with the installed CUDA version, try using ``clang-3.8`` instead:: |
|
+NOTE: If your system does not have a GCC compiler compatible with the installed |
|
+CUDA version (e.g. GCC-5 for CUDA 8), you will see errors at the linker stage.… |
|
+In that case, try using ``clang-3.8`` as the C and C++ compiler instead:: |
|
|
|
+ $ rm -rf CMakeCache.txt CMakeFiles/ |
|
$ export CC=$(which clang-3.8) && export CXX=$(which clang++-3.8) && cmake . … |
|
|
|
After a successfull installation, the ``sphere`` executable will be located |
|
t@@ -157,10 +159,6 @@ The output should look similar to this: |
|
|
|
.. program-output:: ../../sphere --version |
|
|
|
-The build can be verified by running a number of automated tests:: |
|
- |
|
- $ make test |
|
- |
|
The documentation can be read in the `reStructuredText |
|
<http://docutils.sourceforge.net/docs/ref/rst/restructuredtext.html>`_-format … |
|
the ``doc/sphinx/`` folder, or in the HTML or PDF formats in the folders |
|
t@@ -193,10 +191,9 @@ After compiling the ``sphere`` binary, the procedure of a… |
|
a simulation is typically arranged in the following order: |
|
|
|
* Setup of particle assemblage, physical properties and conditions using the |
|
- Python API. |
|
+ Python API (``python/sphere.py``). |
|
* Execution of ``sphere`` software, which simulates the particle behavior as… |
|
function of time, as a result of the conditions initially specified in the |
|
input file. |
|
* Inspection, analysis, interpretation and visualization of ``sphere`` output |
|
in Python, and/or scene rendering using the built-in ray tracer. |
|
- |
|
diff --git a/src/main.cpp b/src/main.cpp |
|
t@@ -85,9 +85,9 @@ int main(const int argc, const char *argv[]) |
|
"| | | |\n" |
|
"| |_| Version: %.2f |\n" |
|
"`-------------------------------------ยด\n" |
|
- " A discrete element method particle dynamics simulator.\n" |
|
+ " A discrete-element method particle dynamics simulator.\n" |
|
" Written by Anders Damsgaard, license GPLv3+.\n" |
|
- " https://cs.au.dk/~adc/\n", VERSION); |
|
+ " https://adamsgaard.dk\n", VERSION); |
|
return 0; |
|
} |
|
