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	tnew time step formula - sphere - GPU-based 3D discrete element method algorith…
	git clone git://src.adamsgaard.dk/sphere
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	---
	commit f6c8394ac2e8e2c86191521693237b39387e8e29
	parent c187341cc547490c3de9c3397af82b2893e0d1d4
	Author: Anders Damsgaard <[email protected]>
	Date: Thu, 19 Jun 2014 14:41:49 +0200

	new time step formula

	Diffstat:
	M python/sphere.py \| 31 ++++++++++++++++++++---------…

	1 file changed, 20 insertions(+), 11 deletions(-)
	---
	diff --git a/python/sphere.py b/python/sphere.py
	t@@ -2312,7 +2312,8 @@ class sim:
	current = 0.0,
	file_dt = 0.05,
	step_count = 0,
	- dt = -1):
	+ dt = -1,
	+ epsilon = 0.01):
	'''
	Set temporal parameters for the simulation. Important: Particle radi…
	physical parameters, and the optional fluid grid need to be set prior …
	t@@ -2332,24 +2333,32 @@ class sim:
	:type step_count: int
	:param dt: The computational time step length [s]
	:type total: float
	+ :param epsilon: Time step multiplier (default = 0.01)
	+ :type epsilon: float
	'''

	- # Computational time step (O'Sullivan et al, 2003)
	- #self.time_dt[0] = 0.17 * \
	- #math.sqrt((4.0/3.0 * math.pi * r_min*3 self.rho[0]) \
	- #/ numpy.amax([self.k_n[:], self.k_t[:]]) )
	- # Computational time step (Zhang and Campbell, 1992)
	if dt > 0:
	self.time_dt[0] = dt
	if (self.np[0] > 0):
	print("Warning: Manually specifying the time step length when "
	+ "simulating particles may produce instabilities.")
	else:
	- r_min = numpy.amin(self.radius)
	- self.time_dt[0] = 0.075 *\
	- math.sqrt((V_sphere(r_min) * self.rho[0]) \
	- / numpy.amax([self.k_n[:], self.k_t[:]]) )
	-
	+ r_min = numpy.min(self.radius)
	+
	+ # Radjaii et al 2011
	+ m_min = self.rho * 4.0/3.0numpy.pir_min**3
	+ k_max = numpy.max([self.k_n[:], self.k_t[:]]))
	+ self.time_dt[0] = epsilon/(numpy.sqrt(k_max/m_min))
	+
	+ # Zhang and Campbell, 1992
	+ #self.time_dt[0] = 0.075 *\
	+ #math.sqrt((V_sphere(r_min) * self.rho[0]) \
	+ #/ numpy.amax([self.k_n[:], self.k_t[:]]) )
	+
	+ # Computational time step (O'Sullivan et al, 2003)
	+ #self.time_dt[0] = 0.17 * \
	+ #math.sqrt((4.0/3.0 * math.pi * r_min*3 self.rho[0]) \
	+ #/ numpy.amax([self.k_n[:], self.k_t[:]]) )

	# Check numerical stability of the fluid phase, by criteria derived by
	# von Neumann stability analysis of the diffusion and advection terms