GopherProxy

	ttransition from effective channel pressure to water pressure - granular-channe…
	git clone git://src.adamsgaard.dk/granular-channel-hydro
	Log
	Files
	Refs
	README
	LICENSE
	---
	commit 7fc6a939b43d9f7333a72bf298b6359747f1b5c7
	parent 9c1dfa711717600fb0bc43f6d6503294c5cddd9b
	Author: Anders Damsgaard Christensen <[email protected]>
	Date: Tue, 31 Jan 2017 21:56:11 -0800

	ttransition from effective channel pressure to water pressure

	Diffstat:
	M 1d-test.py \| 67 ++++++++++++++++++++++++++---…

	1 file changed, 57 insertions(+), 10 deletions(-)
	---
	diff --git a/1d-test.py b/1d-test.py
	t@@ -21,11 +21,12 @@ Ns = 10 # Number of nodes [-]
	Ls = 100e3 # Model length [m]
	#dt = 24.60.60. # Time step length [s]
	#dt = 1. # Time step length [s]
	-dt = 60.60.24 # Time step length [s]
	+dt = 60.*60. # Time step length [s]
	#t_end = 24.60.60.*7. # Total simulation time [s]
	t_end = dt*4
	tol_Q = 1e-3 # Tolerance criteria for the normalized max. residual for Q
	-tol_N_c = 1e-3 # Tolerance criteria for the normalized max. residual for N_c
	+#tol_N_c = 1e-3 # Tolerance criteria for the normalized max. residual for N_c
	+tol_P_c = 1e-3 # Tolerance criteria for the normalized max. residual for P_c
	max_iter = 1e4 # Maximum number of solver iterations before failure
	output_convergence = True

	t@@ -36,6 +37,11 @@ rho_s = 2700. # Sediment density [kg/m^3]
	g = 9.8 # Gravitational acceleration [m/s^2]
	theta = 30. # Angle of internal friction in sediment [deg]

	+# Water source term [m/s]
	+#m_dot = 7.93e-11
	+m_dot = 5.79e-9
	+#m_dot = 4.5e-8
	+
	# Walder and Fowler 1994 sediment transport parameters
	K_e = 0.1 # Erosion constant [-], disabled when 0.0
	#K_d = 6. # Deposition constant [-], disabled when 0.0
	t@@ -75,10 +81,6 @@ N = H0.1rho_i*g # Initial effective stress [Pa]
	p_w = rho_igH - N # Water pressure [Pa], here at floatation
	hydro_pot = rho_wgb + p_w # Hydraulic potential [Pa]

	-#m_dot = 7.93e-11 # Water source term [m/s]
	-m_dot = 5.79e-9 # Water source term [m/s]
	-#m_dot = 4.5e-8 # Water source term [m/s]
	-
	# Initialize arrays for channel segments between nodes
	S = numpy.ones(len(s) - 1)*S_min # Cross-sectional area of channel segments[m^…
	S_max = numpy.zeros_like(S) # Max. channel size [m^2]
	t@@ -87,6 +89,7 @@ W = S/numpy.tan(numpy.deg2rad(theta)) # Assuming no channel…
	Q = numpy.zeros_like(S) # Water flux in channel segments [m^3/s]
	Q_s = numpy.zeros_like(S) # Sediment flux in channel segments [m^3/s]
	N_c = numpy.zeros_like(S) # Effective pressure in channel segments [Pa]
	+P_c = numpy.zeros_like(S) # Water pressure in channel segments [Pa]
	e_dot = numpy.zeros_like(S) # Sediment erosion rate in channel segments [m/s]
	d_dot = numpy.zeros_like(S) # Sediment deposition rate in chan. segments [m/s]
	c_bar = numpy.zeros_like(S) # Vertically integrated sediment content [m]
	t@@ -165,6 +168,7 @@ def flux_and_pressure_solver(S):
	if output_convergence:
	print('it_Q = {}: max_res_Q = {}'.format(it_Q, max_res_Q))

	+ '''
	it_N_c = 0
	max_res_N_c = 1e9 # arbitrary large value
	while max_res_N_c > tol_N_c:
	t@@ -192,6 +196,41 @@ def flux_and_pressure_solver(S):
	'Iterative solution not found for N_c')
	it_N_c += 1
	#import ipdb; ipdb.set_trace()
	+ '''
	+ it_P_c = 0
	+ max_res_P_c = 1e9 # arbitrary large value
	+ while max_res_P_c > tol_P_c:
	+
	+ P_c_old = P_c.copy()
	+ # dP_c/ds = psi - FQ^2/S^{8/3}
	+ #if it_P_c % 2 == 0: # Alternate direction between iterations
	+ #P_c[1:] = psi[1:]*ds[1:] \
	+ #- FQ[1:]2./(S[1:](8./3.))ds[1:] \
	+ #+ P_c[:-1] # Downstream
	+ #else:
	+
	+ #P_c[:-1] = -psi[:-1]*ds[:-1] \
	+ #+ FQ[:-1]2./(S[:-1](8./3.))ds[:-1] \
	+ #+ P_c[1:] # Upstream
	+
	+ P_c[:-1] = -avg_midpoint(psi)*ds[:-1] \
	+ + Favg_midpoint(Q)2./(S[:-1](8./3.))ds[:-1] \
	+ + P_c[1:] # Upstream
	+
	+ # Dirichlet BC at terminus
	+ P_c[-1] = 0.
	+
	+ max_res_P_c = numpy.max(numpy.abs((P_c - P_c_old)/(P_c + 1e-16)))
	+
	+ if output_convergence:
	+ print('it_P_c = {}: max_res_P_c = {}'.format(it_P_c,
	+ max_res_P_c))
	+
	+ if it_P_c >= max_iter:
	+ raise Exception('t = {}, step = {}:'.format(t, step) +
	+ 'Iterative solution not found for P_c')
	+ it_P_c += 1
	+ #import ipdb; ipdb.set_trace()

	#import ipdb; ipdb.set_trace()
	if it_Q >= max_iter:
	t@@ -199,14 +238,16 @@ def flux_and_pressure_solver(S):
	'Iterative solution not found for Q')
	it_Q += 1

	- return Q, N_c
	+ #return Q, N_c
	+ return Q, P_c

	def plot_state(step):
	# Plot parameters along profile
	plt.plot(s_c/1000., S, '-k', label='$S$')
	plt.plot(s_c/1000., S_max, '--k', label='$S_{max}$')
	plt.plot(s_c/1000., Q, '-b', label='$Q$')
	- plt.plot(s_c/1000., N_c/1000., '--r', label='$N_c$')
	+ #plt.plot(s_c/1000., N_c/1000., '--r', label='$N_c$')
	+ plt.plot(s_c/1000., P_c/1000., '--r', label='$P_c$')
	#plt.plot(s, b, ':k', label='$b$')
	#plt.plot(s, b, ':k', label='$b$')
	plt.legend()
	t@@ -224,8 +265,10 @@ s_c = avg_midpoint(s) # Channel section midpoint coordina…
	# Find gradient in hydraulic potential between the nodes
	hydro_pot_grad = gradient(hydro_pot, s)

	-# Find effective pressure in channels [Pa]
	+# Find field values at the middle of channel segments
	N_c = avg_midpoint(N)
	+#P_c = avg_midpoint(P)
	+H_c = avg_midpoint(N)

	# Find fluxes in channel segments [m^3/s]
	Q = channel_water_flux(S, hydro_pot_grad)
	t@@ -263,9 +306,13 @@ while t < t_end:

	#import pdb; pdb.set_trace()
	# Find new fluxes and effective pressures
	- Q, N_c = flux_and_pressure_solver(S)
	+ #Q, N_c = flux_and_pressure_solver(S)
	+ Q, P_c = flux_and_pressure_solver(S)
	# TODO: Q is zig zag

	+ # Find new effective pressure in channel segments
	+ N_c = rho_igH_c - P_c
	+
	#import ipdb; ipdb.set_trace()

	plot_state(step)