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BP5-FD_imcompressible.py
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BP5-FD_imcompressible.py
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# %%
# coding: utf-8
import underworld as uw
from underworld import function as fn
import numpy as np
import math
import os,csv
import mpi4py
import random
comm = mpi4py.MPI.COMM_WORLD
from underworld.scaling import units as u
from underworld.scaling import non_dimensionalise as nd
inputPath = os.path.join(os.path.abspath("."),"BENCHMARK_JGR_3D_128_64_64_dtvep2_Pre1BC1_FixedVStressD3_D1ms_Max50yr_0T1s_shearSameHalf_NoAdv/")
outputPath = inputPath
if uw.mpi.rank==0:
print (uw.__version__)
if not os.path.exists(outputPath):
os.makedirs(outputPath)
uw.mpi.barrier
if uw.mpi.rank==0:
if not os.path.exists(inputPath):
os.makedirs(inputPath)
uw.mpi.barrier
# continue running from specific time step
LoadFromFile = False
Elasticity = True
meshdeform= False
scaling_coefficients = uw.scaling.get_coefficients()
# Define scale criteria
tempMin = 273.*u.degK
tempMax = (500.+ 273.)*u.degK
bodyforce = 3300 * u.kilogram / u.metre**3 * 9.8 * u.meter / u.second**2
velocity = 4e10*u.centimeter/u.year
KL = 100e3*u.meter
Kt = KL/velocity
KT = tempMax
KM = bodyforce * KL**2 * Kt**2
K = 1.*u.mole
lengthScale = 100e3
scaling_coefficients["[length]"] = KL
scaling_coefficients["[time]"] = Kt
scaling_coefficients["[mass]"]= KM
scaling_coefficients["[temperature]"] = KT
scaling_coefficients["[substance]"] = K
gravity = nd(9.81 * u.meter / u.second**2)
R = nd(8.3144621 * u.joule / u.mole / u.degK)
# use low resolution if running in serial
xRes = 128
yRes = 64
zRes = 64
dim = 3
minX = nd( -48.* u.kilometer)
maxX = nd( 48. * u.kilometer)
minY = nd( -50. * u.kilometer)
maxY = nd( 50. * u.kilometer)
minZ = nd( -40. * u.kilometer)
maxZ = nd( 0. * u.kilometer)
stickyAirthick = nd(0. * u.kilometer)
stressNormalFn = nd(25e6*u.pascal)
H = nd(18*u.kilometer)
V0 = nd(1e-6*u.meter/u.second) # nd(4e-9*u.meter/u.second) #
# Rate-and-state properties
miu0 = 0.6
L = nd(0.14*u.meter)
# L = nd(0.01*u.meter)
mu = nd(3.2e10*u.pascal) # elastic modulus
cs = nd(3464*u.meter/u.second) #shear wave velocity
a_max = 0.04 #0.015 #
a0 = 0.004 #0.003 #
b = 0.03 #0.009 #
theta_rock = nd(1e16*u.year) # nd(102000.*u.year) #
pre_f = 1.
BC_f = 1.
V_plate = nd(1e-9*u.meter/u.second)
shearVelocity = 0.5*V_plate #/np.pi*np.arctan(maxX/H) #2*nd(6.3*u.centimeter/u.year)
thickUpCrust = nd(15. * u.kilometer)
BDLayer = nd(0. * u.kilometer)
stickyAirIndex = 0
crustSouthIndex = 1
crustNorthUpIndex = 2
crustNorthLowIndex = 3
crustValleyUpIndex = 4
crustValleyLowIndex = 5
mantleIndex = 6
mantleWeekIndex = 7
crustWeekIndex = 8
fault = 9
if(LoadFromFile == True):
step = 3000
step_out = 100
nsteps = 10000
timestep = float(np.load(inputPath+"time"+str(step).zfill(4)+".npy"))
dt_e = fn.misc.constant(float(np.load(outputPath+"dt"+str(step).zfill(4)+".npy"))) #fn.misc.constant(nd(0.02*u.second)) #
Eqk = True
else:
step = 0
step_out = 100
nsteps = 10000
timestep = 0.
dt_e = fn.misc.constant(nd(1.*u.second)) #fn.misc.constant(nd(0.02*u.year))
Eqk = True
# %%
dt_min= nd(1e-5*u.second)
dt_max = nd(50.*u.year)
mesh = uw.mesh.FeMesh_Cartesian( elementType = ("Q1/dQ0"),
elementRes = (xRes, yRes, zRes),
minCoord = (minX, minY, minZ),
maxCoord = (maxX, maxY, maxZ),
periodic = [False, True, False])
# function to define refined mesh in the fault zone if needed
# not used in the example shown in this ms, but can be implemented easily
def mesh_Uni(section,minX,maxX,res,x1,x2,factor,mi):
# section: mesh to be refined and return
# res: segments numbers, same as resX(Y/Z)
# x1: startpoint of the area to be refined
# x2: endpoint of the area to be refine (x2>x1)
# factor: the ratio of the finest area over the average of the section (maxX-minX)/resX
# mi: power of two ending segments; mi>1 is required
section_cp = np.copy(section)
Uni_all = (maxX-minX)/res
spacing_Refine = Uni_all*factor
N_refine = ((x2-x1)/spacing_Refine)
midPoint = (x1+x2)/2
ratio = 0.5#(x1-minX)/(maxX-x2+x1-minX)
startPoint1 = midPoint-Uni_all*N_refine*ratio
startPoint2 = midPoint+Uni_all*N_refine*(1-ratio)
# print (spacing_Refine,N_refine,startPoint1, startPoint2)
# startPoint2-startPoint1)
for index in range(len(section)):
if section_cp[index]<=startPoint2 and section_cp[index]>=startPoint1:
section[index] = x1 + (section_cp[index]-startPoint1)/Uni_all*spacing_Refine
if section[index]>x2:
section[index] = x2
if section_cp[index]<startPoint1:
section[index] = x1 + (minX-x1)*((section_cp[index]-startPoint1)/(minX-startPoint1))**mi
if section_cp[index]>startPoint2:
section[index] = x2 + (maxX-x2)*((section_cp[index]-startPoint2)/(maxX-startPoint2))**mi
return section
dx = (maxX-minX)/xRes
dy = (maxY-minY)/yRes
dz = (maxZ-minZ)/zRes
interface_z = 0.
mesh.reset()
if (meshdeform == True):
with mesh.deform_mesh():
mesh_Uni(mesh.data[:,0],minX,maxX,xRes,-nd(1000*u.meter),nd(1000*u.meter),0.2,1.2);
dx_min = (maxX-minX)/xRes*0.2
else:
dx_min = dx
velocityField = uw.mesh.MeshVariable( mesh=mesh, nodeDofCount=dim )
pressureField = uw.mesh.MeshVariable( mesh=mesh.subMesh, nodeDofCount=1 )
pressureField0 = uw.mesh.MeshVariable( mesh=mesh.subMesh, nodeDofCount=1 )
stressField = uw.mesh.MeshVariable( mesh=mesh, nodeDofCount=3 )
maskMesh = uw.mesh.MeshVariable( mesh=mesh, nodeDofCount=1 )
temperatureField = uw.mesh.MeshVariable( mesh=mesh, nodeDofCount=1 )
temperatureDotField = uw.mesh.MeshVariable( mesh=mesh, nodeDofCount=1 )
temperatureFieldCopy = uw.mesh.MeshVariable( mesh=mesh, nodeDofCount=1 )
stressField.data[:] = [0.,0.,0.]
velocityField.data[:] = [0.,0.,0.]
pressureField.data[:] = 0.
pressureField0.data[:] = 0.
# send boundary condition information to underworld
iWalls = mesh.specialSets["MinI_VertexSet"] + mesh.specialSets["MaxI_VertexSet"]
jWalls = mesh.specialSets["MinJ_VertexSet"] + mesh.specialSets["MaxJ_VertexSet"]
kWalls = mesh.specialSets["MinK_VertexSet"] + mesh.specialSets["MaxK_VertexSet"]
base = mesh.specialSets["MinK_VertexSet"]
back = mesh.specialSets["MaxJ_VertexSet"]
top = mesh.specialSets["MaxK_VertexSet"]
left = mesh.specialSets["MinI_VertexSet"]
right = mesh.specialSets["MaxI_VertexSet"]
baseFix = mesh.specialSets['Empty']
leftFix = mesh.specialSets['Empty']
rightFix = mesh.specialSets['Empty']
velocityField.data[:] = 0.
# set "easier" intial velocity for the solver to solve
x = fn.input()[0]
conditionVMesh = [(True,-shearVelocity+(x-minX)*2.*shearVelocity/(maxX-minX))]
velocityField.data[:,1] = fn.branching.conditional(conditionVMesh).evaluate(mesh)[:,0]
for index in mesh.specialSets["MaxI_VertexSet"]:
velocityField.data[index] = [0.,shearVelocity,0.]
for index in mesh.specialSets["MinI_VertexSet"]:
velocityField.data[index] = [0.,-shearVelocity,0.]
half_width = pre_f*dx_min
BC_half_width = BC_f*dx_min
for index in mesh.specialSets["MinK_VertexSet"]:
#if mesh.data[index][0]<-BC_half_width:
if mesh.data[index][0]<0.:
velocityField.data[index][1] = -shearVelocity #+ (mesh.data[index][0]-minX)*2.*shearVelocity/(maxX-minX)
#elif mesh.data[index][0]>=-BC_half_width and mesh.data[index][0]<=BC_half_width:
elif mesh.data[index][0]>=0. and mesh.data[index][0]<=BC_half_width:
# velocityField.data[index][1] = -shearVelocity + (mesh.data[index][0]+BC_half_width)*shearVelocity/BC_half_width
velocityField.data[index][1] = -shearVelocity + (mesh.data[index][0])*shearVelocity/BC_half_width
else:
velocityField.data[index][1] = shearVelocity
freeslipBC = uw.conditions.DirichletCondition( variable = velocityField,
indexSetsPerDof = (iWalls,iWalls+base,kWalls) )
swarm = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
pop_control = uw.swarm.PopulationControl(swarm,aggressive=True,particlesPerCell=125)
surfaceSwarm = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
surfaceSwarm2 = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
faultSwarm = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
previousVm = swarm.add_variable( dataType="double", count=3 )
previousVm2 = swarm.add_variable( dataType="double", count=3 )
velA = swarm.add_variable( dataType="double", count=3 )
vel_eff = swarm.add_variable( dataType="double", count=3 )
materialVariable = swarm.add_variable( dataType="int", count=1 )
markSwarm1 = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
markSwarm2 = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
markSwarm3 = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
markSwarm4 = uw.swarm.Swarm( mesh=mesh,particleEscape=True )
plasticStrain = swarm.add_variable( dataType="double", count=1 )
plasticStrain0 = swarm.add_variable( dataType="double", count=1 )
cohesionStrength = swarm.add_variable( dataType="double", count=1 )
cohesionStrength_slip = swarm.add_variable( dataType="double", count=1 )
a_field = swarm.add_variable( dataType="double", count=1 )
L_field = swarm.add_variable( dataType="double", count=1 )
thetaField = swarm.add_variable( dataType="double", count=1 )
swarmYield = swarm.add_variable( dataType="double", count=1 )
#frictionInf = swarm.add_variable( dataType="double", count=1 )
#cohesion = swarm.add_variable( dataType="double", count=1 )
previousStress = swarm.add_variable( dataType="double", count=6 )
faultVariable = faultSwarm.add_variable( dataType="double", count=1)
if(LoadFromFile == False):
#swarmLayout = uw.swarm.layouts.PerCellGaussLayout( swarm=swarm, gaussPointCount=5 )
swarmLayout = uw.swarm.layouts.PerCellSpaceFillerLayout(swarm=swarm,particlesPerCell= 125)
swarm.populate_using_layout( layout=swarmLayout )
if(LoadFromFile == True):
#surfaceSwarm.load(inputPath+"surfaceSwarm"+str(step).zfill(4))
swarm.load(inputPath+"swarm"+str(step).zfill(4))
materialVariable.load(inputPath+"materialVariable"+str(step).zfill(4))
# materialIndex.load(inputPath+"materialIndex"+str(step).zfill(4))
# materialIndex1.load(inputPath+"materialIndex1"+str(step).zfill(4))
# materialIndex2.load(inputPath+"materialIndex2"+str(step).zfill(4))
# materialIndex3.load(inputPath+"materialIndex3"+str(step).zfill(4))
# materialIndex4.load(inputPath+"materialIndex4"+str(step).zfill(4))
velocityField.load(inputPath+"velocityField"+str(step).zfill(4))
# plasticStrain.load(inputPath+"plasticStrain"+str(step).zfill(4))
previousStress.load(inputPath+"previousStress"+str(step).zfill(4))
a_field.load(inputPath+"a_field"+str(step).zfill(4))
L_field.load(inputPath+"L_field"+str(step).zfill(4))
thetaField.load(inputPath+"thetaField"+str(step).zfill(4))
surfaceSwarm.load(inputPath+"surfaceSwarm"+str(step).zfill(4))
surfaceSwarm2.load(inputPath+"surfaceSwarm2"+str(step).zfill(4))
previousVm.load(inputPath+"previousVm"+str(step).zfill(4))
previousVm2.load(inputPath+"previousVm2"+str(step).zfill(4))
# set observation points
y_ob = (maxY+minY)/2.
markSwarm1.add_particles_with_coordinates(np.array([[half_width,y_ob,-nd(1.*u.kilometer)]]))
markSwarm2.add_particles_with_coordinates(np.array([[half_width,y_ob,-nd(10.*u.kilometer)]]))
markSwarm3.add_particles_with_coordinates(np.array([[half_width,y_ob,-nd(20.*u.kilometer)]]))
markSwarm4.add_particles_with_coordinates(np.array([[half_width,y_ob,-nd(28.*u.kilometer)]]))
if(LoadFromFile == False):
xcd3 = 0.
starty = -nd(50.*u.kilometer)
endy = nd(50.*u.kilometer)
faultShape3 = np.array([ (xcd3,starty), (xcd3+half_width,starty), (xcd3+half_width,endy),(xcd3,endy)])
fault3= fn.shape.Polygon( faultShape3 )
starty1 = -nd(30.*u.kilometer)
endy1 = -nd(18.*u.kilometer)
faultShape4 = np.array([ (xcd3,starty1), (xcd3+half_width,starty1), (xcd3+half_width,endy1),(xcd3,endy1)])
fault4= fn.shape.Polygon( faultShape4 )
#fn.misc.max(-coordz*nd(28e6*u.pascal/u.kilometer)-nd(100e6*u.pascal), -coordz*nd(10e6*u.pascal/u.kilometer))
if LoadFromFile == False:
coordz = fn.input()[2]
coordy = fn.input()[1]
condMat = [(fault3,fault),
(coordz<nd(-40.*u.kilometer), crustNorthLowIndex),
(True,crustNorthUpIndex)]
materialVariable.data[:] = fn.branching.conditional(condMat).evaluate(swarm)
rangey0 = (coordy>nd(-30.*u.kilometer)) & (coordy<nd(30.*u.kilometer))
range_L = (coordy<=nd(-30.*u.kilometer)) & (coordy>=nd(-32.*u.kilometer))
range_R = (coordy>=nd(30.*u.kilometer)) & (coordy<=nd(32.*u.kilometer))
rangez0 = (coordz>nd(-16.*u.kilometer)) & (coordz<nd(-4.*u.kilometer))
rangez1 = coordz>nd(-40.*u.kilometer)
Vi = nd(0.03*u.meter/u.second)
theta0 = L/V_plate
theta1 = L/Vi
####>>>>>>>>>>>Earthquake
# condition_theta = [ #(coordz<nd(-18.*u.kilometer), nd(1.9e16*u.year)),
# (fault3,nd(0.029*u.year)),
# (True, nd(1.9e16*u.year))]
# range_lf = coordy<=nd(50.*u.kilometer) and coordy>=nd(-50.*u.kilometer)
condition_theta = [ ((fault4 & rangez0),theta1 ),
((fault3 & rangez1),theta0),
(True, nd(1.9e20*u.year))]
thetaField.data[:] = fn.branching.conditional(condition_theta).evaluate(swarm)
#thetaField.save(inputPath+"thetaField0"+str(step).zfill(4))
condition_a = [ ((range_L & (coordz<-nd(2.*u.kilometer)) & (coordz>=-nd(18.*u.kilometer))),a0-(a_max-a0)*(coordy+nd(30.*u.kilometer))/nd(2.*u.kilometer)),
((range_R & (coordz<-nd(2.*u.kilometer)) & (coordz>=-nd(18.*u.kilometer))),a0+(a_max-a0)*(coordy-nd(30.*u.kilometer))/nd(2.*u.kilometer)),
((rangey0 & (coordz<-nd(2.*u.kilometer)) & (coordz>=-nd(4.*u.kilometer))),a0-(-a_max+a0)*(coordz+nd(4.*u.kilometer))/nd(2.*u.kilometer)),
((rangey0 & (coordz<-nd(4.*u.kilometer)) & (coordz>=-nd(16.*u.kilometer))),a0),
((rangey0 & (coordz<-nd(16.*u.kilometer)) & (coordz>=-nd(18.*u.kilometer))),a0-(a_max-a0)*(coordz+nd(16.*u.kilometer))/nd(2.*u.kilometer)),
(True, a_max)]
# condition_a = [ (True, a_max)]
# condition_a = [(coordz>-nd(15.*u.kilometer),a0),
# (True, a_max)]
a_field.data[:] = fn.branching.conditional(condition_a).evaluate(swarm)
condition_Vi = [ ((fault4 & rangez0),Vi),
(True, V_plate)]
ViFn = fn.branching.conditional(condition_Vi)
condition_L = [ ((fault4 & rangez0),nd(0.13*u.meter)),
(True, nd(0.14*u.meter))]
L_field.data[:] = fn.branching.conditional(condition_L).evaluate(swarm)
kernalX = ViFn/(2.*V0)*fn.math.exp((miu0 + b*fn.math.log(V0/ViFn))/a_field)
frictionFn0 = a_field*fn.math.log(kernalX+fn.math.sqrt(kernalX*kernalX+1.))
#eta_factor = 2.*mu/cs
stressShearFn = frictionFn0*stressNormalFn
previousStress.data[:] = 1e-20 #0.1*stressNormalFn#
previousStress.data[:,3] = stressShearFn.evaluate(swarm)[:,0] # + eta_factor*V_plate ( + for static only) #nd(0.7e7*u.pascal) #
####>>>>>>>>>>>Earthquake
countz=zRes*2
zcoord = np.linspace(minZ,maxZ, countz)
surfacePoints = np.zeros((countz,3))
for k in range(countz):
surfacePoints[k,0] = dx_min#xcoord[j]
surfacePoints[k,1] = y_ob
surfacePoints[k,2] = zcoord[k]
surfaceSwarm.add_particles_with_coordinates( surfacePoints )
county=yRes*2
ycoord = np.linspace(minY+nd(10*u.kilometer), maxY-nd(10*u.kilometer), county)
surfacePoints2 = np.zeros((county,3))
for k in range(county):
surfacePoints2[k,0] = dx_min#xcoord[j]
surfacePoints2[k,1] = ycoord[k]
surfacePoints2[k,2] = nd(-10*u.kilometer)
surfaceSwarm2.add_particles_with_coordinates( surfacePoints2 )
# maskCoreFn1 = fn.branching.conditional([(materialIndex1>1e8, 1.),
# (True, 0.)])
# maskCoreFn2 = fn.branching.conditional([(materialIndex2>1e8, 1.),
# (True, 0.)])
# maskCoreFn3 = fn.branching.conditional([(materialIndex3>1e8, 1.),
# (True, 0.)])
# maskCoreFn4 = fn.branching.conditional([(materialIndex4>1e8, 1.),
# (True, 0.)])
# maskCoreFn = fn.branching.conditional([(materialIndex>1e8, 1.),
# (True, 0.)])
strainRateFn = fn.tensor.symmetric( velocityField.fn_gradient )
strainRate_2ndInvariantFn = fn.tensor.second_invariant(strainRateFn)+nd(1e-18/u.second)
plasticStrain0.data[:] = 0.
VpFn = 2.*strainRate_2ndInvariantFn*half_width
thetaFieldFn = L_field/VpFn+(thetaField-L_field/VpFn)*fn.math.exp(-VpFn/L_field*dt_e)
if Eqk == True:
#kernalX = VpFn/(2.*V0)*fn.math.exp((miu0 + b*fn.math.log(V0*thetaField/L))/a_field)
#frictionFn = a_field*fn.math.log(kernalX+fn.math.sqrt(kernalX*kernalX+1.))
frictionFn = miu0 + a_field*fn.math.log(VpFn/V0) +b*fn.math.log(V0*thetaField/L_field)
yieldStressFn = frictionFn*stressNormalFn#pressureField nd(1e6*u.pascal)+
densityMap0 = { fault : nd( 2670. * u.kilogram / u.metre**3),
crustNorthUpIndex : nd( 2670. * u.kilogram / u.metre**3),
crustNorthLowIndex : nd( 2670. * u.kilogram / u.metre**3),
}
densityFn = fn.branching.map( fn_key = materialVariable, mapping = densityMap0 )
z_hat=( 0.0, 0.0, -1.0 )
buoyancyFn = densityFn * z_hat *gravity
if (Elasticity == True):
mappingDictViscosity = { fault : nd(5e29 * u.pascal * u.second),
crustNorthUpIndex : nd(5e29 * u.pascal * u.second),
crustNorthLowIndex : nd(5e29 * u.pascal * u.second)}
viscosityMapFn1 = fn.branching.map( fn_key = materialVariable,
mapping = mappingDictViscosity )
alpha = viscosityMapFn1 / mu # viscoelastic relaxation time
viscoelasticViscosity = ( viscosityMapFn1 * dt_e ) / (alpha + dt_e) # effective viscosity
visElsMap = { fault : viscoelasticViscosity,
crustNorthUpIndex : viscoelasticViscosity,
crustNorthLowIndex : viscoelasticViscosity}
viscosityMapFn = fn.branching.map( fn_key = materialVariable,
mapping = visElsMap )
strainRate_effective = strainRateFn + 0.5*previousStress/(mu*dt_e)
strainRate_effective_2ndInvariant = fn.tensor.second_invariant(strainRate_effective)+nd(1e-18/u.second)
yieldingViscosityFn = 0.5 * yieldStressFn / strainRate_effective_2ndInvariant
#viscosityFn = fn.exception.SafeMaths( fn.misc.max(fn.misc.min(yieldingViscosityFn,
# viscosityMapFn), min_viscosity))
#viscosityFn = fn.exception.SafeMaths( fn.misc.min(yieldingViscosityFn,viscosityMapFn))
yieldFnMap = { fault : yieldingViscosityFn,
crustNorthUpIndex : nd(1e20*u.pascal),
crustNorthLowIndex : nd(1e20*u.pascal)}
yieldFn = fn.branching.map( fn_key = materialVariable,
mapping = yieldFnMap )
viscosityFn = ( fn.misc.min(yieldFn,viscosityMapFn))
# contribution from elastic rheology
tauHistoryFn = viscosityFn / ( mu * dt_e ) * previousStress
# stress from all contributions, including elastic,viscous,plastic (if yielded)
allStressFn = 2. * viscosityFn * strainRate_effective#
allStressFn_2nd = fn.tensor.second_invariant(allStressFn)
visStrainRateFn = allStressFn/(2.*viscosityMapFn1)
elaStrainRateFn = (allStressFn-previousStress)/dt_e/(2.*mu)
plaStrainRateFn = strainRateFn - visStrainRateFn - elaStrainRateFn
plaStrainRateFn_2nd = fn.tensor.second_invariant(plaStrainRateFn)
vis_vp = viscosityMapFn1*allStressFn_2nd/(2.*viscosityMapFn1*plaStrainRateFn_2nd+allStressFn_2nd)
swarmYield_Cond = [(viscosityMapFn>viscosityFn,1.),
(True,0.)]
swarmYieldFn = fn.branching.conditional(swarmYield_Cond)
#plaRate2nd = strainRate_2ndInvariant*swarmYieldFn
#plaStrainRateFn_2nd = fn.tensor.second_invariant(plaStrainRateFn)
#elaStrainRateFn_2nd = fn.tensor.second_invariant(elaStrainRateFn)
#visStrainRateFn_2nd = fn.tensor.second_invariant(visStrainRateFn)
plaIncrement = plaStrainRateFn_2nd*swarmYieldFn
#elaIncrement = elaStrainRateFn_2nd*swarmYieldFn
#visIncrement = visStrainRateFn_2nd*swarmYieldFn
stressMapFn = allStressFn
LHS_fn = densityFn/dt_e
RHS_fn = densityFn*previousVm/dt_e
stokes = uw.systems.Stokes(velocityField = velocityField,
pressureField = pressureField,
voronoi_swarm = swarm,
conditions = freeslipBC,
fn_viscosity = viscosityFn,
#fn_bodyforce = buoyancyFn,
fn_bodyforce = buoyancyFn+RHS_fn,
fn_stresshistory = tauHistoryFn)
massMatrixTerm = uw.systems.sle.MatrixAssemblyTerm_NA__NB__Fn(
assembledObject = stokes._kmatrix,
integrationSwarm = stokes._constitMatTerm._integrationSwarm,
fn = LHS_fn,
mesh = mesh)
# Create solver & solve
solver = uw.systems.Solver(stokes)
# %%
# use "lu" direct solve if running in serial
if(uw.mpi.size==1):
solver.set_inner_method("lu")
else:
solver.set_inner_method('mg')
solver.set_penalty(1e-3)
#solver.options.ksp_rtol=1e-8
inner_rtol = 1e-5
solver.set_inner_rtol(inner_rtol)
solver.set_outer_rtol(10*inner_rtol)
# solver.options.ksp_rtol=1e-5
# solver.options.scr.ksp_rtol = 1.0e-5
surfaceArea = uw.utils.Integral(fn=1.0,mesh=mesh, integrationType='surface', surfaceIndexSet=top)
surfacePressureIntegral = uw.utils.Integral(fn=pressureField, mesh=mesh, integrationType='surface', surfaceIndexSet=top)
def pressure_calibrate():
(area,) = surfaceArea.evaluate()
(p0,) = surfacePressureIntegral.evaluate()
offset = p0/area
#print "Zeroing pressure using mean upper surface pressure {}".format( offset )
pressureField.data[:] -= offset
#plasticStrain0.data[:] = plaIncrement.evaluate(swarm) # plaRate2nd.evaluate(swarm)
def nonLinearSolver(step, nl_tol=1e-2, nl_maxIts=10):
# a hand written non linear loop for stokes, with pressure correction
er = 1.0
its = 0 # iteration count
v_old = velocityField.copy() # old velocityField
while er > nl_tol and its < nl_maxIts:
v_old.data[:] = velocityField.data[:]
solver.solve(nonLinearIterate=False)
# pressure correction for bob (the feed back pressure)
(area,) = surfaceArea.evaluate()
(p0,) = surfacePressureIntegral.evaluate()
offset = p0/area
#print "Zeroing pressure using mean upper surface pressure {}".format( offset )
pressureField.data[:] -= offset
#plasticStrain0.data[:] = plaIncrement.evaluate(swarm)
# calculate relative error
absErr = uw.utils._nps_2norm(velocityField.data-v_old.data)
magT = uw.utils._nps_2norm(v_old.data)
er = absErr/magT
if uw.mpi.rank==0.:
print ("tolerance=", er,"iteration times=",its)
uw.mpi.barrier
its += 1
G_star = mu/(1.-0.5)
k_stiff = (2./3.1415926)*G_star/dx_min
# see Herrendorfer et al., 2018 for the defination of de_thea, dt_w, dt_vep
pusei = 0.25*fn.math.pow((k_stiff*L_field/(a_field*stressNormalFn)-(b-a_field)/a_field),2.)-k_stiff*L/(a_field*stressNormalFn)
pusei_Cond = [(pusei>0,a_field*stressNormalFn/(k_stiff*L_field-(b-a_field)*stressNormalFn)),
(True,1.-(b-a_field)*stressNormalFn/(k_stiff*L_field))]
puseiFn = fn.branching.conditional(pusei_Cond)
dt_theta = fn.misc.min(fn.misc.constant(0.2),puseiFn)
# condw = [(plasticStrain0>0,dt_theta *L_field/VpFn),
# (True,dt_theta *L_field/VpFn)]
# dt_wFn0 = fn.branching.conditional(condw)
# dt_wFn = fn.view.min_max(dt_wFn0)
dt_wFn = fn.view.min_max(0.3*L_field/VpFn)
#dt_wFn.evaluate(swarm)
#dt_w = dt_wFn.min_global()
dt_hFn = fn.view.min_max(thetaField*0.2)
#dt_vepFn = fn.view.min_max(0.2*vis_vp/mu)
dt_vepFn = fn.view.min_max(0.2*vis_vp/mu)
#delta_Fn = (yieldingViscosityFn-allStressFn_2nd)**2./pressureField**2.
#surfaceArea = uw.utils.Integral(fn=1.0,mesh=mesh)
#surface_dF_Integral = uw.utils.Integral(fn=delta_Fn, mesh=mesh)
advMat = uw.systems.SwarmAdvector( swarm=swarm, velocityField=velocityField, order=2 )
advSurf = uw.systems.SwarmAdvector( swarm=surfaceSwarm, velocityField=velocityField, order=2 )
advSurf2 = uw.systems.SwarmAdvector( swarm=surfaceSwarm2, velocityField=velocityField, order=2 )
#The root mean square Velocity
velSquared = uw.utils.Integral( fn.math.dot(velocityField,velocityField), mesh )
area = uw.utils.Integral( 1., mesh )
Vrms = math.sqrt( velSquared.evaluate()[0]/area.evaluate()[0] )
time_factor = nd(1*u.year)
def update():
dt = dt_e.value
velA.data[:] = velocityField.evaluate(swarm)
vel_eff.data[:] = 1./4.*(velA.data[:]+2.*previousVm.data[:]+previousVm2.data[:])
# vel_eff.data[:] = 1./2.*(velA.data[:]+1.*previousVm.data[:])
previousVm2.data[:] = np.copy(previousVm.data[:])
previousVm.data[:] = np.copy(velA.data[:])
# swarm advection can be ignored in earthquake cycle simulations due to small displacement with respect to grid size
# with swarm.deform_swarm():
# swarm.data[:] += vel_eff.data[:]*dt
#update theta value in the RS frictional relationship
condition_theta = { fault : thetaFieldFn,
crustNorthUpIndex : theta_rock,
crustNorthLowIndex : theta_rock
}
thetaField.data[:] = fn.branching.map( fn_key = materialVariable,
mapping = condition_theta ).evaluate(swarm)
stressMapFn_data = stressMapFn.evaluate(swarm)
previousStress.data[:] = stressMapFn_data[:]
# advMat.integrate(dt)
advSurf.integrate(dt)
advSurf2.integrate(dt)
#advMark.integrate(dt)
pop_control.repopulate()
dt_wFn.reset()
dt_wFn.evaluate(swarm)
dt_w = dt_wFn.min_global()
dt_hFn.reset()
dt_hFn.evaluate(swarm)
dt_h = dt_hFn.min_global()
dt_vepFn.reset()
dt_vepFn.evaluate(swarm)
dt_vep = dt_vepFn.min_global()
V_fault = fn.view.min_max(VpFn)
V_fault.evaluate(mesh.subMesh)
Vp_max = V_fault.max_global()
# dt0 = np.min([dt_max,dt_vep,dt_w])
# dt0 = np.min([dt_max,dt_vep,dt_w,2*dt_e.value])
dt0 = np.min([dt_max,dt_vep])
# dt_e.value = np.max([dt0,dt_min,0.5*dt_e.value])
dt_e.value = np.max([dt0,dt_min])
return timestep+dt, step+1
stressSample = np.zeros([4,1])
thetaSample = np.zeros([4,1])
fricSample = np.zeros([4,1])
velSample = np.zeros([4,1])
plsticIncrement = np.zeros([5,1])
Dissipation = np.zeros([9,1])
yieldHis = np.zeros([4,1])
if step == 0:
title = ['step','time','F1','F2','F3','F4','dt_e','V1','V2','V3','V4']
with open(outputPath+'Sample.csv', 'w') as f:
csv_write = csv.writer(f)
csv_write.writerow(title)
vdotv = uw.utils.Integral(fn.math.dot(velocityField,velocityField),mesh=mesh)
meshInt = uw.utils.Integral(fn=1.0,mesh=mesh)
Vrms = shearVelocity
V_rate_old = 0.
jump_step = 1.
while step<nsteps:
solver.solve( nonLinearIterate=True, nonLinearTolerance=1e-3, nonLinearMaxIterations=15,callback_post_solve = pressure_calibrate)
picard_h = solver.get_nonLinearStats()
if picard_h.picard_residual>0.005:
if uw.mpi.rank==0:
print('more itr is called')
uw.mpi.barrier()
# dt_e.value = 0.9*dt_e.value
solver.solve( nonLinearIterate=True, nonLinearTolerance=1e-3, nonLinearMaxIterations=5,callback_post_solve = pressure_calibrate)
# picard_h = solver.get_nonLinearStats()
dt_inner = advMat.get_max_dt()
while dt_inner < dt_e.value :
dt_e.value = 0.5*dt_e.value
#nonLinearSolver(step, nl_tol=1e-3, nl_maxIts=30)
solver.solve(nonLinearIterate=True, nonLinearTolerance=1e-3, nonLinearMaxIterations=30,callback_post_solve = pressure_calibrate)
dt_inner = advMat.get_max_dt()
visMin = 0.
VelMM = fn.view.min_max(fn.math.abs(velocityField[1])*maskMesh)
VelMM.evaluate(mesh)
Vrms_new = VelMM.max_global()
#Vrms = Vrms_new
meshStress = uw.mesh.MeshVariable( mesh, 1 )
projectorStress = uw.utils.MeshVariable_Projection( meshStress, allStressFn[3], type=0 )
projectorStress.solve()
# output figure to file at intervals = steps_output
if step %step_out == 0 or step == nsteps-1:
#Important to set the timestep for the store object here or will overwrite previous step
if (Elasticity == True):
previousStress.save(outputPath+"previousStress"+str(step).zfill(4))
'''
meshFriction = uw.mesh.MeshVariable( mesh, 1 )
projectorStress = uw.utils.MeshVariable_Projection( meshFriction, frictionFn, type=0 )
projectorStress.solve()
frictionInf.data[:] = frictionFn.evaluate(swarm)
'''
mesh.save(outputPath+"mesh"+str(step).zfill(4))
swarm.save(outputPath+"swarm"+str(step).zfill(4))
materialVariable.save(outputPath+"materialVariable"+str(step).zfill(4))
a_field.save(outputPath+"a_field"+str(step).zfill(4))
L_field.save(outputPath+"L_field"+str(step).zfill(4))
thetaField.save(outputPath+"thetaField"+str(step).zfill(4))
previousVm.save(outputPath+"previousVm"+str(step).zfill(4))
previousVm2.save(outputPath+"previousVm2"+str(step).zfill(4))
#swarmYield.save(inputPath+"yieldSwarm"+str(step).zfill(4))
if step % 10 == 0 :
meshStress.save(outputPath+"meshStress"+str(step).zfill(4))
velocityField.save(outputPath+"velocityField"+str(step).zfill(4))
if uw.mpi.rank==0:
np.save(outputPath+"time"+str(step).zfill(4),timestep)
np.save(outputPath+"dt"+str(step).zfill(4),dt_e.value)
# np.save(outputPath+"plstRateAll0"+str(step).zfill(4),plstRateAll0)
uw.mpi.barrier()
dicMesh = { 'elements' : mesh.elementRes,
'minCoord' : mesh.minCoord,
'maxCoord' : mesh.maxCoord}
fo = open(outputPath+"dicMesh"+str(step).zfill(4),'w')
fo.write(str(dicMesh))
fo.close()
stressMM = fn.view.min_max(fn.math.abs(meshStress))
stressMM.evaluate(markSwarm2)
stressSample[1] = stressMM.max_global()
stressMM = fn.view.min_max(fn.math.abs(meshStress))
stressMM.evaluate(markSwarm3)
stressSample[2] = stressMM.max_global()
velMM = fn.view.min_max(fn.math.abs(velocityField[1]))
velMM.evaluate(markSwarm2)
velSample[3] = velMM.max_global()
velMM = fn.view.min_max(fn.math.abs(velocityField[1]))
velMM.evaluate(markSwarm3)
velSample[2] = velMM.max_global()
V_fault = fn.view.min_max(VpFn)
V_fault.evaluate(mesh.subMesh)
velSample[1] = V_fault.max_global()
if uw.mpi.rank==0:
SP_output = [step,timestep,stressSample[0,0],stressSample[1,0],stressSample[2,0],stressSample[3,0],dt_e.value,velSample[0,0],velSample[1,0],velSample[2,0],velSample[3,0]]
with open(outputPath+'Sample.csv', 'a') as f:
csv_write = csv.writer(f)
csv_write.writerow(SP_output)
uw.mpi.barrier()
surfaceSwarm.save(outputPath+"surfaceSwarm"+str(step).zfill(4))
surfaceSwarm2.save(outputPath+"surfaceSwarm2"+str(step).zfill(4))
if uw.mpi.rank==0:
print('step = {0:6d}; time = {1:.3e};'.format(step,timestep/nd(1.*u.year)))
uw.mpi.barrier()
timestep, step = update()