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SChimney_WDamp2DLx25.py
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SChimney_WDamp2DLx25.py
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# -*- coding: utf-8 -*-
"""
Created on Wed May 1 16:14:58 2024
@author: Lawrence H.W
This is the python version of the 2D full coupled porosity wave code
"""
from scipy.io import savemat
import numpy as np
import matplotlib.pyplot as plt
import sys
#from time import time
# Constants and Parameters
nt = 3000
phi0 = 0.1
rhos = 2
rhof = 1
mut = 0.1 # total rock (solid+fluid) shear viscosity
muf = 1 # shear viscosity of the fluid
kperm0 = 1 # permeability coefficient
#eta2mut = 10
etas0 = 1 #eta2mut * mut / phi0 # background bulk viscosity
eta2mut = etas0*phi0/mut
npower = 3.0 # power exponent of the permeability-porosity relationship
Lx = 25 #10*np.sqrt(etas0 * kperm0 / muf)
Rxy = 2
Ly = Lx * Rxy
gravity = 1 # simplified gravity value
clength = 1
ctime_unit = clength * phi0 / kperm0 / (rhos - rhof) / gravity * muf
tsc = ctime_unit
ttotal = 8 * ctime_unit
R = 100
Vplastic_on = 0
pkc = 3.0
p0 = 4.05
tau0 = 18
ntau = 2
pk0 = pkc
alpha_tau = 0
mp = 2
Lambda = 10
relax_eta = 0.1
relax_kp = 0.1
# Numerics
nx = 25 * 4 - 1
ny = 25 * 8 - 1
dx = Lx / nx
dy = Ly / ny
x = np.linspace(0.5 * dx, Lx - 0.5 * dx, nx)
y = np.linspace(0.5 * dy, Ly - 0.5 * dy, ny)
xx, yy = np.meshgrid(x, y,indexing='ij')
nout= 10
ploton=1
CN = 0.5;# Crank-Nicolson CN=0.5, Backward Euler CN=0.0
force_iter = 0.5*ny;##1*ny;
iterMax1 = 100*ny;
Vdmp = 3.14*2;
eta_b = 0.5;
cnt = 50; #check/calculate PT residule every cnt iteration
cnt1 = 500; #output residule every cnt iteration
epsi = 1e-5;
Xd = 4.1
Ptsc = 2.1
Vsc = 1.5
lambda_p= 0.01 #2*rhos*gravity*dy;
# Initial Conditions
phi = phi0*np.ones((nx, ny))
#phi = phi0 * (1 + 3 * np.exp(-((yy - 5) / 0.5) ** 2))
#initialize phi with a inclusion that has high porosity.
xa = 1
phiA= 3
radc=((xx - 0.5*Lx) /8/xa) ** 2 + ((yy - 0.2*Ly)/xa)**2;
phi[radc<1]=phi0+phi0*phiA
#phi = phi0 * (1 + 3 * np.exp(-(((xx - 5) / 1.5) ** 2 + ((yy - 10) / 0.8) ** 2)))
# initialize phi with an elliptical area that has high value
#phi[yy < 5] = phi0 * (1 + 3)
Pt = np.zeros((nx, ny))
Pe = np.zeros((nx, ny))
Pd = np.zeros((nx, ny))
Vx = np.zeros((nx + 1, ny))
Vy = np.zeros((nx, ny + 1))
div = np.zeros((nx, ny))
div_old = np.zeros((nx, ny))
Tauxx = np.zeros((nx, ny))
Tauyy = np.zeros((nx, ny))
Tauxy = np.zeros((nx + 1, ny + 1))
RVx = np.zeros((nx-1, ny))
RVy = np.zeros((nx, ny-1))
qDx = np.zeros((nx+1, ny))
qDy = np.zeros((nx, ny+1))
divqD=np.zeros((nx,ny))
dphidt = np.zeros((nx, ny))
tau = np.zeros((nx, ny))
phi_old = phi.copy();
F = np.zeros((nx, ny))
ap = np.ones((nx, ny))
kperm = kperm0 * np.ones((nx, ny))
etas = etas0 * np.ones((nx, ny))
eta_phi = etas * phi0 / phi
kp_muf =kperm/muf;
rhoBG = rhos * (1 - phi0) + rhof * phi0
#etas(cond2)=9*etas0; % not for shear viscosity, but only for bulk viscosity
#kperm(cond3)=0.1*kperm0;
#eta_phi = etas0*ones(nx,ny);
phi0f = phi.copy();
dt_fact = 1e-1*ctime_unit;
dt_init = 1e-5*ctime_unit; #initial guess of dt
dt = dt_init;
phi0bc = phi0 #mean(phi(:,end));
phi0bot = phi[:,0];
# Constants and parameters initialization (define these as needed)
# Example: nt, ny, nx, CN, mut, eta_b, Ptsc, etc.
ndim = 2
betaqD = muf * (1 - phi0) / kperm0
# Calculate dtV
dtV = min(dx, dy)**2 / 2.1 / (1.0 + eta_b) / mut / ndim / Vsc
# Calculate dmp1 and dmp2
dmp1 = -1 / (2 * betaqD) + np.sqrt(1 + 4 * betaqD) / (2 * betaqD)
dmp2 = 1 / dmp1
qDy[:, [0, -1]] = dmp1 * (rhos - rhof) * gravity * (1.0 - phi0bc) * kperm0 / muf * (phi0bc / phi0)**npower
resid = 1e5;
residRVy = 1e5;
residRPt = 1e5;
residRPe = 1e5;
time = 0;
TimeS=np.zeros(nt);
# Time integration
#tstart = time()
#plt.show()
for it in range(1,nt+1):
# Update equations and other operations
# Placeholder for actual simulation logic
# Time-stepping loop (assuming this is inside a loop over time steps)
if it < 2:
iterMax = 200 * ny
else:
iterMax = iterMax1
np.copyto(phi_old, phi)
np.copyto(div_old, div)
#div_old = div.copy() % it will create new array every time!
#div_old = div.copy()
for iter in range(1, iterMax + 1):
Tauxy1 = 0.5 * (Tauxy[:-1, :] + Tauxy[1:, :])
Tauxy2 = 0.5 * (Tauxy1[:, :-1] + Tauxy1[:, 1:])
tau = np.sqrt(0.5 * (Tauxx**2 + Tauyy**2 + 2.0 * Tauxy2**2))
div = (np.diff(Vx, axis=0) / dx + np.diff(Vy, axis=1) / dy)
phi = phi_old + dt * (1 - phi) * (CN * div_old + (1 - CN) * div)
if Vplastic_on == 1:
F = np.exp((np.abs(-alpha_tau * tau + Pe - p0) / pk0) ** mp - 1.0) * (1.0 + (tau / tau0) ** ntau) * pk0 - pk0
f = pk0 * np.log(F / pk0 + 1.0)
ind1 = F >= 0
f[~ind1] = 0.0
A = 2.0 * Lambda * f * np.exp(f / pk0) / pk0
ap = np.ones_like(phi)
Pd = np.zeros_like(phi)
ap[ind1] = A[ind1] + 1.0
Pd[ind1] = A[ind1] * (alpha_tau * tau[ind1] + p0)
Pd = Pd / ap
eta_phi = phi0 * etas / phi / ap * relax_eta + eta_phi * (1.0 - relax_eta)
else:
eta_phi = etas * phi0 / phi * (1.0 + 0.5 * (1.0 / R - 1.0) * (1.0 - np.tanh((Pe) / lambda_p))) * relax_eta + eta_phi * (1.0 - relax_eta)
rhot = rhof * phi + rhos * (1 - phi) - rhoBG
rhoPe = 1 / (1 - phi) / eta_phi
kp_muf = np.exp(np.log(kperm / muf * (phi / phi0) ** npower) * relax_kp + np.log(kp_muf) * (1 - relax_kp))
Vpref = np.sqrt(kp_muf * eta_phi)
Xd1=np.minimum(Xd * (1 + 1.5*(iter / ny)), 2 * Xd)
dtau = dx / Vpref / Xd1
dtauPe = dtau / rhoPe
dtauPe[1:-1, 1:-1] = np.min([dtauPe[1:-1, 1:-1], dtauPe[:-2, 1:-1], dtauPe[2:, 1:-1], dtauPe[1:-1, :-2], dtauPe[1:-1, 2:]], axis=0)
dtauqDx = np.min([dtau[:-1, :], dtau[1:, :]], axis=0)
dtauqDy = np.min([dtau[:, :-1], dtau[:, 1:]], axis=0)
RPt = -div - (Pe - Pd) / eta_phi / (1 - phi)
Ptsc1 = np.minimum(Ptsc * (1 + (iter / ny)), 5 * Ptsc)
dtPt = 4.1 * mut * (1 + eta_b) / max(nx, ny) / Ptsc1
Pt += dtPt * RPt
Tauxx = 2.0 * mut * (np.diff(Vx, axis=0) / dx - div / 3.0 - eta_b * RPt)
Tauyy = 2.0 * mut * (np.diff(Vy, axis=1) / dy - div / 3.0 - eta_b * RPt)
Tauxy[1:-1, 1:-1] = mut * (np.diff(Vx[1:-1, :], axis=1) / dy + np.diff(Vy[:, 1:-1], axis=0) / dx)
RVx = RVx * (1 - Vdmp / nx) + (np.diff(Tauxx - Pt, axis=0) / dx + np.diff(Tauxy[1:-1, :], axis=1) / dy)
rho_avy = 0.5 * (rhot[:, :-1] + rhot[:, 1:])
RVy = RVy * (1 - Vdmp / ny) + (np.diff(Tauyy - Pt, axis=1) / dy + np.diff(Tauxy[:, 1:-1], axis=0) / dx - rho_avy * gravity)
Vx[1:-1, :] += dtV * RVx
Vy[:, 1:-1] += dtV * RVy
kpx_muf = 0.5 * (kp_muf[:-1, :] + kp_muf[1:, :])
kpy_muf = 0.5 * (kp_muf[:, :-1] + kp_muf[:, 1:])
RqDx = (kpx_muf * (np.diff(Pe - Pt, axis=0) / dx) - dmp2 * qDx[1:-1, :])
RqDy = (kpy_muf * (np.diff(Pe - Pt, axis=1) / dy - (rhof - rhoBG) * gravity) - dmp2 * qDy[:, 1:-1])
qDx[1:-1, :] += dtauqDx * RqDx / betaqD
qDy[:, 1:-1] += dtauqDy * RqDy / betaqD
divqD = np.diff(qDx, axis=0) / dx + np.diff(qDy, axis=1) / dy
RPe = (divqD - dmp1 * (Pe - Pd) / (1 - phi) / eta_phi)
Pe += dtauPe * RPe
if iter % cnt == 0:
residRVy = np.linalg.norm(RVy) / len(RVy.ravel())
residRPe = np.linalg.norm(RPe) / len(RPe.ravel())
residRPt = np.linalg.norm(RPt) / len(RPt.ravel())
resid = max(residRVy, residRPe, residRPt)
if iter % cnt1 == 0:
#print(f'At Step {it},iter={iter} residRVy={residRVy:5.3e},residRPe={residRPe:5.3e},residRPt={residRPt:5.3e}')
print('at step {:4d}, iter={}, residRVy={:5.3e}, residRPe={:5.3e}, residRPt={:5.3e}'.format(it, iter, residRVy, residRPe, residRPt))
if residRVy==np.nan:
print('At step {it},iter={:5d}. resid=nan. Exit now.'.format(it,iter))
sys.exit()
if resid > 1e5:
#print(f'At Step {it}, Error is larger than 1e5 at iteration {iter}, resid={resid}')
print(f'At Step {it}, Error is larger than 1e5 at iteration {iter}, resid={resid}')
sys.exit()#return
if resid < epsi and iter >= force_iter:
break
time = time+ dt
TimeS[it] = time
max_div = np.max(np.abs(div))
dt = min(0.01 * tsc, dt_fact / (1e-10 + max_div))
#print(f'Step={it:4d} converge , resid={resid:e}, dt={dt:e}, max_div={max_div:e} at iterations={iter:4d}(={iter/ny:3.1f} *ny)')
print('Step={:4d} converge,time={:5.2f}({:5.2f} δt), resid={:e}, dt={:e}, max_div={:e} at iterations={:4d}(={:4.1f} *ny)'.format(it, time,time/tsc,resid, dt, max_div, iter, iter/ny))
print('****maxporosity={:e},minporosity={:e},maxbulkv={:e},minbulk={:e},,maxperm={:e},minperm={:e}'.format(phi.max(),phi.min(),eta_phi.max(),eta_phi.min(),kp_muf.max(),kp_muf.min()))
phi[phi<0.2*phi0]=0.2*phi0
# Assuming 'it', 'nout', 'x', 'y', 'Pe', 'phi0f', 'nx', 'phi', 'Ly', 'eta_phi', 'iter', 'iterMax1', 'resid', and 'epsi' are defined
if it % nout == 0 and 1==0: # not plotting
plt.figure(2)
plt.suptitle(f'step = {it}')
# Subplot 1: Peclet number
plt.subplot(2, 2, 1)
plt.gca().set_aspect(2) # pbaspect([1 2 1])
plt.pcolor(xx, yy, Pe) # Transpose Pe to match MATLAB's behavior
plt.axis('image')
plt.colorbar()
plt.title(f'Pe at step = {it}')
# Subplot 2: Porosity profiles
plt.subplot(2, 2, 2)
plt.plot(phi0f[int(nx/2), :], y, 'g', phi[int(nx/2), :], y, 'r')
plt.axis([0, 0.5, 0, Ly])
#'plt.gca().set_aspect(0.5) # pbaspect([0.5 1 0.5])
plt.title('Porosity profiles')
plt.xlabel('X axis')
# Subplot 3: Bulk Viscosity
plt.subplot(2, 2, 3)
plt.contourf(xx, yy, eta_phi) # Transpose eta_phi to match MATLAB's behavior
plt.axis('image')
plt.colorbar()
plt.title('Bulk Viscosity')
# Subplot 4: Porosity
plt.subplot(2, 2, 4)
plt.pcolor(xx, yy, phi) # Transpose phi to match MATLAB's behavior
plt.axis('image')
plt.colorbar()
plt.title('Porosity')
plt.xlabel('X axis')
#plt.draw()
# Save the status
if it % nout == 0 or it==1:
# np.save(f'step{it}', {'x': x, 'y': y, 'Pe': Pe, 'phi': phi, 'eta_phi': eta_phi}) # save npy file
#filename = 'step' + str(it) + '.mat'
filename = 'step{}.mat'.format(it)
savemat(filename, {'x': x, 'y': y, 'Pe': Pe, 'phi': phi, 'eta_phi': eta_phi})
if ploton==1:
#plt.figure();plt.pcolor(x,y,phi.T);plt.axis("scaled");plt.colorbar()#plt.ion();plt.show();
plt.figure()#%figsize=(10, 5)
plt.subplot(1, 2, 1)
#plt.contour(x, y, phi.T, cmap='viridis')
plt.pcolor(x, y, phi.T,shading='auto', cmap='viridis')
plt.axis("scaled")
plt.colorbar()
plt.title('step {}:({:5.2f}δt)'.format(it,time/tsc))
plt.xlabel('X')
plt.ylabel('Y')
plt.subplot(1, 2, 2)
plt.plot(phi[int(nx / 2), :], y, 'r')
plt.title('Porosity Profile')
plt.savefig(f'step{it}.jpg')
plt.close()
if it > 10 and iter == iterMax1 and resid > epsi:
#print(f'Not converged at {iter:5d} iteration. Save and return now.')
print('Not converged at {:5d} iteration. Save and return now.'.format(iter))
filename = 'step{}.mat'.format(it)
savemat(filename, {'x': x, 'y': y, 'Pe': Pe, 'phi': phi, 'eta_phi': eta_phi})
#return
sys.exit()
# Check for convergence and exit if necessary
if time>ttotal:
print('The time reachs ttotal={:5.2f}({:5.2f} δt).Now exit'.format(time,time/tsc))
sys.exit()
#telapsed = time() - tstart
#£print('Elapsed time is {:.4f} seconds'.format(telapsed))