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flaps.py
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###############################################################################
#
# +++++ + +++++ +++++ +++++
# + + + + + + +
# +++ + +++++ +++++ +++++
# + + + + + +
# + +++++ + + + +++++
#
###############################################################################
import numpy as np
import sys as sys
import scipy
import scipy.sparse as sps
from scipy.sparse.linalg import *
import time as timing
import matplotlib.pyplot as plt
from scipy import sparse
from numba import jit
###############################################################################
from basis_functions import *
from density import *
from viscosity import *
from analytical_solution import *
from gravity_vector import *
from compute_gravity_at_point import *
from compute_strain_rate1 import *
from compute_strain_rate2 import *
from compute_strain_rate3 import *
from export_to_vtu import *
from quadrature_setup import *
from compute_normals import *
from define_mapping import *
from compute_element_center_coords import *
from compute_rho_eta_fields import *
from compute_errors import *
from project_pressure_on_Q2 import *
from constants import *
###############################################################################
# list of available Earth density and viscosity profiles
###############################################################################
planet_is_Earth=False
rho_model=0 # constant
#rho_model=1 # PREM
#rho_model=2 # STW105
#rho_model=3 # AK135F
eta_model=0 # constant
#eta_model=1 # civs12 a
#eta_model=2 # civs12 b
#eta_model=3 # stho08
#eta_model=4 # yohk01
###############################################################################
# list of available Mars density and viscosity profiles
###############################################################################
planet_is_Mars=False
use_eta_steinberger=False
use_eta_samuelA=False
use_eta_samuelB=False
###############################################################################
planet_is_4DEarth=False
###############################################################################
print("+=================================================")
print("+=================================================")
print(" xxxxx x xxxxx xxxxx xxxxx ")
print(" x x x x x x x ")
print(" xxx x xxxxx xxxxx xxxxx ")
print(" x x x x x x ")
print(" x xxxxx x x x xxxxx ")
print("+=================================================")
print("+=================================================")
ndim=2 # number of dimensions
mV=9 # number of nodes making up an element
mP=4 # number of nodes making up an element
ndofV=2 # number of velocity degrees of freedom per node
ndofP=1 # number of pressure degrees of freedom
###############################################################################
# reading parameters from command line, or not
###############################################################################
if int(len(sys.argv) == 12):
exp = int(sys.argv[1])
nelr = int(sys.argv[2])
visu = int(sys.argv[3])
nqperdim = int(sys.argv[4])
mapping = int(sys.argv[5])
xi = int(sys.argv[6])
etablobstar = float(sys.argv[7])
rhoblobstar = float(sys.argv[8])
zblob = float(sys.argv[9])
Rblob = float(sys.argv[10])
etalithstar = float(sys.argv[11])
if mapping==1: mapping='Q1'
if mapping==2: mapping='Q2'
if mapping==3: mapping='Q3'
if mapping==4: mapping='Q4'
if mapping==5: mapping='Q5'
if mapping==6: mapping='Q6'
print(sys.argv)
else:
# exp=0: cyl benchmark
# exp=1: aquarium
exp = 0
nelr = 32 # Q1 cells!
visu = 1
nqperdim = 3
mapping = 'Q2'
xi = 6
etablobstar = 1
rhoblobstar = 0.9
zblob = 4900e3
Rblob = 400e3
etalithstar = 1
###########################################################
if exp==0: # plane strain annulus benchmark
R1=1.
R2=2.
rho_m=0.
g0=1.
eta_ref=1
eta_m=1
vel_unit=1
velunit=' '
surface_free_slip=False
bottom_free_slip=False
compute_gravity=False
nstep=1
rhoc=0
gravity_model=0
rho_model=0
eta_model=0
use_elemental_density=False
use_elemental_viscosity=False
axisymmetric=False
self_gravitation=False
solve_stokes=True
else:
R1=3400e3
R2=6400e3
g0=10.
eta_ref=1e21
eta_m=1e21
rho_m=4000.
vel_unit=0.01/year
velunit='cm/year'
nstep=1
rhoc=6000
gravity_model=0
surface_free_slip=True
bottom_free_slip=False # not implemented
use_elemental_density=True
use_elemental_viscosity=True
axisymmetric=True
self_gravitation=False
solve_stokes=True
dt=50*year
compute_gravity=False
nel_phi = 100
debug=False
compute_sr1=False
compute_sr3=False
###############################################################################
###############################################################################
start = timing.time()
if planet_is_Earth:
R1=3480e3
R2=6371e3
g0=9.81
print('max depth',R2-R1)
#--------------------------------------
if eta_model==1 or eta_model==2: #civs12a,b
# reading data from civs12
# file is 153 lines long
# first 51 lines are viscA, then 51 lines are viscB
# and last 51 lines are depths, from 0 to 2900km
# I have removed all ",&"
viscA_civs12 = np.empty(51,dtype=np.float64)
viscB_civs12 = np.empty(51,dtype=np.float64)
depths_civs12 = np.empty(51,dtype=np.float64)
f = open('DATA/EARTH/eta_civs12.ascii','r')
counter=0
for line in f:
line=line.strip()
columns=line.split()
if counter<51:
viscA_civs12[counter]=columns[0]
elif counter<102:
viscB_civs12[counter-51]=columns[0]
else:
depths_civs12[counter-102]=columns[0]
counter+=1
depths_civs12[:]=np.flip(depths_civs12)
viscA_civs12[:]=np.flip(viscA_civs12)
viscB_civs12[:]=np.flip(viscB_civs12)
np.savetxt('civs12.ascii',np.array([depths_civs12,viscA_civs12,viscB_civs12]).T)
print(' -> read eta_civs12.ascii ok')
#-----------------
if eta_model==3: #stho08
# reading data from Steinberger & Holmes 2008
# file counts 22 lines
# first column is number between 0 and 1 (normalised radii)
# second column is viscosity
# I have added a last line R=1, eta=1e24
depths_stho08 = np.empty(23,dtype=np.float64)
visc_stho08 = np.empty(23,dtype=np.float64)
f = open('DATA/EARTH/eta_stho08.ascii','r')
counter=0
for line in f:
line=line.strip()
columns=line.split()
depths_stho08[counter]=columns[0]
visc_stho08[counter]=columns[1]
counter+=1
#end for
depths_stho08[:]=6371e3*(1-depths_stho08[:])
depths_stho08[:]=np.flip(depths_stho08)
visc_stho08[:]=np.flip(visc_stho08)
np.savetxt('stho08.ascii',np.array([depths_stho08,visc_stho08]).T)
print(' -> read eta_stho08.ascii ok')
#-----------------
if rho_model==3: #AK135F:
depth_ak135f = np.empty(145,dtype=np.float64)
rho_ak135f = np.empty(145,dtype=np.float64)
f = open('DATA/EARTH/rho_ak135f.ascii','r')
counter=0
for line in f:
line=line.strip()
columns=line.split()
depth_ak135f[counter]=columns[0]
rho_ak135f[counter]=columns[1]
counter+=1
#end for
depth_ak135f[:]*=1000
rho_ak135f[:]*=1000
np.savetxt('density_ak135f.ascii',np.array([depth_ak135f,rho_ak135f]).T)
print(' -> read rho_ak135f.ascii ok')
#-----------------
if rho_model==2: #STW105
depth_stw105 = np.empty(750,dtype=np.float64)
rho_stw105 = np.empty(750,dtype=np.float64)
f = open('DATA/EARTH/rho_stw105.ascii','r')
counter=0
for line in f:
line=line.strip()
columns=line.split()
depth_stw105[counter]=columns[0]
rho_stw105[counter]=columns[1]
counter+=1
#end for
depth_stw105[:]=6371e3-depth_stw105[:]
depth_stw105[:]=np.flip(depth_stw105)
rho_stw105[:]=np.flip(rho_stw105)
np.savetxt('density_stw105.ascii',np.array([depth_stw105,rho_stw105]).T)
print(' -> read rho_stw105.ascii ok')
#--------------------------------------
if grav_model==1: #prem
depth_prem= np.empty(44,dtype=np.float64)
g_prem = np.empty(44,dtype=np.float64)
print("read EARTH data...........................(%.3fs)" % (timing.time() - start))
###############################################################################
###############################################################################
start = timing.time()
if planet_is_Mars:
R1=1700e3
R2=3390e3
g0=3.71 #https://en.wikipedia.org/wiki/Mars
if use_steinberger:
R1=R2-1967e3
R_disc1 = R2-49.5e3
R_disc2 = R2-1111.5e3
R_disc3 = R2-1160e3
R_disc4 = R2-1951.5e3
eta_max=1e25
if use_samuelA:
R1=1839.5976879540331e3
R_disc1 = 3317.7417442558781e3
R_disc2 = 2836.6008937146739e3
R_disc3 = 2350.4998282194360e3
R_disc4 = 1918.9611272185618e3
eta_max=1e25
if use_samuelB:
R1=1624.2975658322634e3
R_disc1 = 3324.3388640802909e3
R_disc2 = 3090.3851276356227e3
R_disc3 = 2313.0549710614014e3
R_disc4 = 1822.5068139999998e3
eta_max=1e25
print("read MARS data............................(%.3fs)" % (timing.time() - start))
###############################################################################
###############################################################################
start = timing.time()
if planet_is_4DEarth:
R1=3400e3
R2=6400e3
###############################################################################
# quadrature points and associated weights
###############################################################################
start = timing.time()
nqel,qcoords_r,qcoords_s,qweights=quadrature_setup(nqperdim)
print("quadrature setup..........................(%.3fs)" % (timing.time() - start))
###############################################################################
# grid point setup
###############################################################################
start = timing.time()
#xV,yV,rad,theta=mesh_nodes(nelr,nelt,axisymmetric,R1,R2)
if not axisymmetric:
nelt=xi*nelr
nel=nelr*nelt
nnr=nelr+1
nnt=nelt
NV=nnr*nnt # number of V nodes
xV=np.zeros(NV,dtype=np.float64)
yV=np.zeros(NV,dtype=np.float64)
rad=np.zeros(NV,dtype=np.float64)
theta=np.zeros(NV,dtype=np.float64)
Louter=2.*math.pi*R2
Lr=R2-R1
sx=Louter/float(nelt)
sz=Lr/float(nelr)
counter=0
for j in range(0,nnr):
for i in range(0,nelt):
xV[counter]=i*sx
yV[counter]=j*sz
counter += 1
counter=0
for j in range(0,nnr):
for i in range(0,nnt):
x_i=xV[counter]
y_i=yV[counter]
t=x_i/Louter*2.*math.pi
xV[counter]=math.cos(t)*(R1+y_i)
yV[counter]=math.sin(t)*(R1+y_i)
rad[counter]=R1+y_i
#theta[counter]=np.arctan2(yV[counter],xV[counter])
theta[counter]=np.pi/2-np.arctan2(yV[counter],xV[counter])
if theta[counter]<0.:
theta[counter]+=2.*math.pi
counter+=1
else:
nelt=xi*nelr
nel=nelr*nelt
nnr=nelr+1
nnt=nelt+1
NV=nnr*nnt # number of V nodes
xV=np.zeros(NV,dtype=np.float64)
yV=np.zeros(NV,dtype=np.float64)
rad=np.zeros(NV,dtype=np.float64)
theta=np.zeros(NV,dtype=np.float64)
Louter=math.pi*R2
Lr=R2-R1
sx=Louter/float(nelt)
sz=Lr/float(nelr)
counter=0
for j in range(0,nnr):
for i in range(0,nnt):
xV[counter]=i*sx
yV[counter]=j*sz
counter += 1
counter=0
for j in range(0,nnr):
for i in range(0,nnt):
x_i=xV[counter]
yi=yV[counter]
t=math.pi/2-x_i/Louter*math.pi
xV[counter]=math.cos(t)*(R1+yi)
yV[counter]=math.sin(t)*(R1+yi)
rad[counter]=R1+yi
theta[counter]=np.pi/2-np.arctan2(yV[counter],xV[counter])
if i==0:
theta[counter]=0
xV[counter]=0
if i==nnt-1:
theta[counter]=np.pi
xV[counter]=0
counter+=1
if debug:
np.savetxt('grid.ascii',np.array([xV,yV,theta]).T,header='# x,y')
print("coordinate arrays.........................(%.3fs)" % (timing.time() - start))
###############################################################################
# build iconQ1 array
###############################################################################
start = timing.time()
iconQ1 =np.zeros((4,nel),dtype=np.int32)
if not axisymmetric:
counter = 0
for j in range(0, nelr):
for i in range(0, nelt):
icon1=counter
icon2=counter+1
icon3=i+(j+1)*nelt+1
icon4=i+(j+1)*nelt
if i==nelt-1:
icon2-=nelt
icon3-=nelt
iconQ1[0,counter] = icon2
iconQ1[1,counter] = icon1
iconQ1[2,counter] = icon4
iconQ1[3,counter] = icon3
counter += 1
#end for
#end for
else:
counter = 0
for j in range(0,nelr):
for i in range(0,nelt):
iconQ1[0,counter] = i + j * (nelt + 1)
iconQ1[1,counter] = i + 1 + j * (nelt + 1)
iconQ1[2,counter] = i + 1 + (j + 1) * (nelt + 1)
iconQ1[3,counter] = i + (j + 1) * (nelt + 1)
counter += 1
if debug: export_Q1_mesh_to_vtu(NV,nel,xV,yV,iconQ1)
print("build iconQ1..............................(%.3fs)" % (timing.time() - start))
###############################################################################
# now that the grid has been built as if it was a Q1 grid,
# we can simply use these same points to arrive at a Q2
# connectivity array with 4 times less elements.
###############################################################################
start = timing.time()
nelr=nelr//2
nelt=nelt//2
nel=nel//4
if not axisymmetric:
NP=nelt*(nelr+1)
else:
NP=(nelt+1)*(nelr+1)
NfemV=NV*ndofV # Total number of degrees of V freedom
NfemP=NP*ndofP # Total number of degrees of P freedom
Nfem=NfemV+NfemP # total number of dofs
h_r=(R2-R1)/nelr # radial resolution
if axisymmetric:
total_volume=4*np.pi/3*(R2**3-R1**3)
else:
total_volume=np.pi*(R2**2-R1**2)
rhoblob=rhoblobstar*rho_m
print(' -------------------')
print(' nelr=',nelr,' ; nelt=',nelt,' ; nel=',nel)
print(' NfemV=',NfemV,' ; NfemP=',NfemP, '; Nfem=',Nfem)
print(' nqel=',nqel)
print(' mapping=',mapping)
print(' axisymmetric=',axisymmetric)
print(' exp=',exp)
print(' xi=',xi)
print(' h_r=',h_r)
print(' eta_model=',eta_model)
print(' rho_model=',rho_model)
print(' compute_gravity=',compute_gravity)
if exp>0:
print(' rhoblob=',rhoblob)
print(' Rblob=',Rblob)
print(' zblob=',zblob)
print(' nel_phi=',nel_phi)
print(' -------------------')
print("compute nelr,nelt,nel.....................(%.3fs)" % (timing.time() - start))
###############################################################################
# connectivity
###############################################################################
start = timing.time()
iconV =np.zeros((mV,nel),dtype=np.int32,order='F')
iconP =np.zeros((mP,nel),dtype=np.int32,order='F')
if not axisymmetric:
counter = 0
for j in range(0, nelr):
for i in range(0, nelt):
iconV[0,counter]=2*counter+2 +2*j*nelt
iconV[1,counter]=2*counter +2*j*nelt
iconV[2,counter]=iconV[1,counter]+4*nelt
iconV[3,counter]=iconV[1,counter]+4*nelt+2
iconV[4,counter]=iconV[0,counter]-1
iconV[5,counter]=iconV[1,counter]+2*nelt
iconV[6,counter]=iconV[2,counter]+1
iconV[7,counter]=iconV[5,counter]+2
iconV[8,counter]=iconV[5,counter]+1
if i==nelt-1:
iconV[0,counter]-=2*nelt
iconV[7,counter]-=2*nelt
iconV[3,counter]-=2*nelt
#print(j,i,counter,'|',iconV[0:mV,counter])
counter += 1
#end for
#end for
counter = 0
for j in range(0, nelr):
for i in range(0, nelt):
icon1=counter
icon2=counter+1
icon3=i+(j+1)*nelt+1
icon4=i+(j+1)*nelt
if i==nelt-1:
icon2-=nelt
icon3-=nelt
iconP[0,counter] = icon2
iconP[1,counter] = icon1
iconP[2,counter] = icon4
iconP[3,counter] = icon3
counter += 1
#end for
#end for
else:
counter = 0
for j in range(0,nelr):
for i in range(0,nelt):
iconV[0,counter]=(i)*2+1+(j)*2*nnt -1
iconV[1,counter]=(i)*2+3+(j)*2*nnt -1
iconV[2,counter]=(i)*2+3+(j)*2*nnt+nnt*2 -1
iconV[3,counter]=(i)*2+1+(j)*2*nnt+nnt*2 -1
iconV[4,counter]=(i)*2+2+(j)*2*nnt -1
iconV[5,counter]=(i)*2+3+(j)*2*nnt+nnt -1
iconV[6,counter]=(i)*2+2+(j)*2*nnt+nnt*2 -1
iconV[7,counter]=(i)*2+1+(j)*2*nnt+nnt -1
iconV[8,counter]=(i)*2+2+(j)*2*nnt+nnt -1
counter += 1
#end for
#end for
counter = 0
for j in range(0,nelr):
for i in range(0,nelt):
iconP[0,counter]=i+j*(nelt+1)
iconP[1,counter]=i+1+j*(nelt+1)
iconP[2,counter]=i+1+(j+1)*(nelt+1)
iconP[3,counter]=i+(j+1)*(nelt+1)
counter += 1
#end for
#end for
print("connectivity array........................(%.3fs)" % (timing.time() - start))
###############################################################################
#now that I have both connectivity arrays I can easily build xP,yP (Q1 space)
###############################################################################
start = timing.time()
xP=np.empty(NP,dtype=np.float64) # x coordinates
yP=np.empty(NP,dtype=np.float64) # y coordinates
for iel in range(0,nel):
xP[iconP[0,iel]]=xV[iconV[0,iel]]
xP[iconP[1,iel]]=xV[iconV[1,iel]]
xP[iconP[2,iel]]=xV[iconV[2,iel]]
xP[iconP[3,iel]]=xV[iconV[3,iel]]
yP[iconP[0,iel]]=yV[iconV[0,iel]]
yP[iconP[1,iel]]=yV[iconV[1,iel]]
yP[iconP[2,iel]]=yV[iconV[2,iel]]
yP[iconP[3,iel]]=yV[iconV[3,iel]]
print("compute xP,yP.............................(%.3fs)" % (timing.time() - start))
###############################################################################
# find out nodes on hull
###############################################################################
start = timing.time()
hull=np.zeros(NV,dtype=bool)
for i in range(0,NV):
if rad[i]/R1<1+eps:
hull[i]=True
if rad[i]/R2>1-eps:
hull[i]=True
if axisymmetric and xV[i]/R2<eps:
hull[i]=True
print("flag nodes on hull........................(%.3fs)" % (timing.time() - start))
###############################################################################
# flag surface nodes and elements
###############################################################################
start = timing.time()
surfaceV=np.zeros(NV,dtype=bool)
outer_element=np.zeros(nel,dtype=bool)
cmbV=np.zeros(NV,dtype=bool)
inner_element=np.zeros(nel,dtype=bool)
for i in range(0,NV):
if rad[i]/R2>1-eps:
surfaceV[i]=True
if rad[i]/R1<1+eps:
cmbV[i]=True
for iel in range(0,nel):
if surfaceV[iconV[2,iel]]:
outer_element[iel]=True
if cmbV[iconV[0,iel]]:
inner_element[iel]=True
outerQ2=np.zeros(NV,dtype=bool)
innerQ2=np.zeros(NV,dtype=bool)
for iel in range(0,nel):
if outer_element[iel]:
outerQ2[iconV[2,iel]]=True
outerQ2[iconV[3,iel]]=True
outerQ2[iconV[6,iel]]=True
if inner_element[iel]:
innerQ2[iconV[0,iel]]=True
innerQ2[iconV[1,iel]]=True
innerQ2[iconV[4,iel]]=True
if axisymmetric:
leftV=np.zeros(NV,dtype=bool)
for i in range(0,NV):
if xV[i]<eps and yV[i]>0: leftV[i]=True
print("flag surf and cmb nodes+elts..............(%.3fs)" % (timing.time() - start))
###############################################################################
# compute normal vectors
###############################################################################
start = timing.time()
normal_type=1
nx,ny=compute_normals(normal_type,NV,xV,yV,mV,nqel,surfaceV,hull,\
R1,R2,eps,iconV,axisymmetric,rad,theta,\
qcoords_r,qcoords_s,qweights,)
if debug:
np.savetxt('normals.ascii',np.array([xV[surfaceV],yV[surfaceV],\
nx[surfaceV],ny[surfaceV],theta[surfaceV]]).T)
print("compute surface normals...................(%.3fs)" % (timing.time() - start))
###############################################################################
# define boundary conditions
###############################################################################
start = timing.time()
bc_fix = np.zeros(Nfem,dtype=bool)
bc_val = np.zeros(Nfem,dtype=np.float64)
for i in range(0,NV):
if rad[i]/R1<1+eps:
bc_fix[i*ndofV] = True ; bc_val[i*ndofV] = velocity_x(xV[i],yV[i],R1,R2,exp)
bc_fix[i*ndofV+1] = True ; bc_val[i*ndofV+1] = velocity_y(xV[i],yV[i],R1,R2,exp)
if rad[i]/R2>(1-eps) and not surface_free_slip:
bc_fix[i*ndofV] = True ; bc_val[i*ndofV] = velocity_x(xV[i],yV[i],R1,R2,exp)
bc_fix[i*ndofV+1] = True ; bc_val[i*ndofV+1] = velocity_y(xV[i],yV[i],R1,R2,exp)
#vertical wall x=0
if axisymmetric and xV[i]/R1<eps:
bc_fix[i*ndofV] = True ; bc_val[i*ndofV] = 0 #u=0
if rad[i]/R2>1-eps:
bc_fix[i*ndofV+1] = True ; bc_val[i*ndofV+1] = 0 #also v=0 for 2 pts
#bc_fix[i*ndofV] = False
print("defining boundary conditions..............(%.3fs)" % (timing.time() - start))
###############################################################################
# compute array for assembly
###############################################################################
start = timing.time()
ndofV_el=mV*ndofV
local_to_globalV=np.zeros((ndofV_el,nel),dtype=np.int32)
for iel in range(0,nel):
for k1 in range(0,mV):
for i1 in range(0,ndofV):
ikk=ndofV*k1 +i1
m1 =ndofV*iconV[k1,iel]+i1
local_to_globalV[ikk,iel]=m1
print("compute local_to_global...................(%.3fs)" % (timing.time() - start))
###############################################################################
# fill I,J arrays
###############################################################################
start = timing.time()
bignb=nel*( (mV*ndofV)**2 + 2*(mV*ndofV*mP) )
I=np.zeros(bignb,dtype=np.int32)
J=np.zeros(bignb,dtype=np.int32)
V=np.zeros(bignb,dtype=np.float64)
counter=0
for iel in range(0,nel):
for ikk in range(ndofV_el):
m1=local_to_globalV[ikk,iel]
for jkk in range(ndofV_el):
m2=local_to_globalV[jkk,iel]
I[counter]=m1
J[counter]=m2
counter+=1
for jkk in range(0,mP):
m2 =iconP[jkk,iel]+NfemV
I[counter]=m1
J[counter]=m2
counter+=1
I[counter]=m2
J[counter]=m1
counter+=1
print("fill I,J arrays...........................(%.3fs)" % (timing.time() - start))
##############################################################################################
##############################################################################################
##############################################################################################
# time stepping
##############################################################################################
##############################################################################################
##############################################################################################
for istep in range(0,nstep):
print('**************************************************')
print('******************** istep='+str(istep)+' *********************')
print('**************************************************')
###############################################################################
###############################################################################
start = timing.time()
if mapping=='Q1': mmapping=4
if mapping=='Q2': mmapping=9
if mapping=='Q3': mmapping=16
if mapping=='Q4': mmapping=25
if mapping=='Q5': mmapping=36
if mapping=='Q6': mmapping=49
xmapping,zmapping=define_mapping(mapping,mmapping,xV,yV,iconV,nel,\
axisymmetric,rad,theta,nelt)
print(spacing+" -> xmapping (m,M) %.2e %.2e " %(np.min(xmapping),np.max(xmapping)))
print(spacing+" -> zmapping (m,M) %.2e %.2e " %(np.min(zmapping),np.max(zmapping)))
if debug:
np.savetxt('xzmapping'+mapping+'.ascii',np.array([xmapping[0,:],zmapping[0,:]]).T)
export_mapping_points_to_vtu(mapping,mmapping,xmapping,zmapping)
export_quadrature_points_to_vtu(nqperdim,nqel,qcoords_r,qcoords_s,mapping,\
xmapping,zmapping)
print("define mapping............................(%.3fs)" % (timing.time() - start))
###############################################################################
# compute element center coordinates
###############################################################################
start = timing.time()
xc,zc,thetac=compute_element_center_coords(nel,mapping,xmapping,zmapping)
print(spacing+" -> xc (m,M) %.2e %.2e " %(np.min(xc),np.max(xc)))
print(spacing+" -> zc (m,M) %.2e %.2e " %(np.min(zc),np.max(zc)))
print("compute center coords.....................(%.3fs)" % (timing.time() - start))
###############################################################################
# compute elemental and nodal viscosity+density fields for 1st timestep only
###############################################################################
start = timing.time()
if istep==0:
density_elemental,density_nodal,viscosity_elemental,viscosity_nodal=\
compute_rho_eta_fields(mV,NV,nel,xc,zc,iconV,R1,R2,rho_m,eta_m,eta_model,\
rho_model,exp,rhoblobstar,zblob,Rblob)
print(spacing+" -> eta_e (m,M) %.2e %.2e " %(np.min(viscosity_elemental),np.max(viscosity_elemental)))
print(spacing+" -> rho_e (m,M) %.2e %.2e " %(np.min(density_elemental),np.max(density_elemental)))
print(spacing+" -> eta_n (m,M) %.2e %.2e " %(np.min(viscosity_nodal),np.max(viscosity_nodal)))
print(spacing+" -> rho_n (m,M) %.2e %.2e " %(np.min(density_nodal),np.max(density_nodal)))
if debug:
np.savetxt('xycenter'+mapping+'.ascii',np.array([xc,yc,density_elemental,viscosity_elemental]).T)
print("compute rho+eta fields....................(%.3fs)" % (timing.time() - start))
###############################################################################
# compute area and volume of elements
# note that for the volume calculation we only consider the elements x>0
###############################################################################
start = timing.time()
area=np.zeros(nel,dtype=np.float64)
vol=np.zeros(nel,dtype=np.float64)
massq = np.zeros(nel*nqel,dtype=np.float64)
radq = np.zeros(nel*nqel,dtype=np.float64)
thetaq = np.zeros(nel*nqel,dtype=np.float64)
zq = np.zeros(nel*nqel,dtype=np.float64)
rhoq = np.zeros(nel*nqel,dtype=np.float64)
etaq = np.zeros(nel*nqel,dtype=np.float64)
counterq=0
jcb=np.zeros((2,2),dtype=np.float64)
for iel in range(0,nel):
for kq in range(0,nqel):
rq=qcoords_r[kq]
sq=qcoords_s[kq]
weightq=qweights[kq]
NNNV=NNN(rq,sq,mapping)
dNNNVdr=dNNNdr(rq,sq,mapping)
dNNNVds=dNNNds(rq,sq,mapping)
xq=np.dot(NNNV[:],xmapping[:,iel])
yq=np.dot(NNNV[:],zmapping[:,iel])
zq[counterq]=yq
radq[counterq]=np.sqrt(xq**2+yq**2)
thetaq[counterq]=np.pi/2-np.arctan2(yq,xq)
jcb[0,0]=np.dot(dNNNVdr[:],xmapping[:,iel])
jcb[0,1]=np.dot(dNNNVdr[:],zmapping[:,iel])
jcb[1,0]=np.dot(dNNNVds[:],xmapping[:,iel])
jcb[1,1]=np.dot(dNNNVds[:],zmapping[:,iel])
jcob = np.linalg.det(jcb)
area[iel]+=jcob*weightq
massq[counterq]=density_elemental[iel]*weightq*jcob*2*np.pi*xq
if xq>0: vol[iel]+=jcob*weightq*2*np.pi*xq
if use_elemental_density:
rhoq[counterq]=density_elemental[iel]
else:
rhoq[counterq]=density(xq,yq,R1,R2,rho_m,rho_model,\
exp,rhoblobstar,zblob,Rblob)
if use_elemental_viscosity:
etaq[counterq]=viscosity_elemental[iel]
else:
etaq[counterq]=viscosity(xq,yq,R1,R2,eta_m,eta_model)
counterq+=1
#end for
#end for
if axisymmetric:
print(spacing+" -> total volume (meas) %.12e | nel= %d" %(vol.sum(),nel))
print(spacing+" -> total volume (anal) %.12e" %(total_volume))
else:
print(spacing+" -> area (m,M) %.6e %.6e " %(np.min(area),np.max(area)))
print(spacing+" -> total area (meas) %.12e | nel= %d" %(area.sum(),nel))
print(spacing+" -> total area (anal) %e " %(total_volume))
print(spacing+" -> rhoq (m,M) %.3e %.3e " %(np.min(rhoq),np.max(rhoq)))
print(spacing+" -> etaq (m,M) %.3e %.3e " %(np.min(etaq),np.max(etaq)))
print(spacing+" -> massq (m,M) %.3e %.3e " %(np.min(massq),np.max(massq)))
print(spacing+" -> total mass (meas) %.12e | nel= %d" %(np.sum(density_elemental*vol),nel))
print("sanity check.............................. %.3fs | %d" % (timing.time()-start,Nfem))
###############################################################################
# build FE matrix
###############################################################################
start = timing.time()
f_rhs = np.zeros(NfemV,dtype=np.float64)
h_rhs = np.zeros(NfemP,dtype=np.float64)
dNNNVdx = np.zeros(mV,dtype=np.float64)
dNNNVdy = np.zeros(mV,dtype=np.float64)
jcb=np.zeros((2,2),dtype=np.float64)
if axisymmetric:
#c_mat=np.array([[2,0,0,0],[0,2,0,0],[0,0,2,0],[0,0,0,1]],dtype=np.float64)
c_mat=np.array([[4/3,-2/3,-2/3,0],[-2/3,4/3,-2/3,0],[-2/3,-2/3,4/3,0],[0,0,0,1]],dtype=np.float64)
b_mat= np.zeros((4,ndofV*mV),dtype=np.float64) # gradient matrix B
N_mat= np.zeros((4,ndofP*mP),dtype=np.float64) # matrix
else:
c_mat=np.array([[2,0,0],[0,2,0],[0,0,1]],dtype=np.float64)
b_mat= np.zeros((3,ndofV*mV),dtype=np.float64) # gradient matrix B
N_mat= np.zeros((3,ndofP*mP),dtype=np.float64) # matrix
counter=0
counterq=0
for iel in range(0,nel):
if not solve_stokes: break
f_el =np.zeros((mV*ndofV),dtype=np.float64)
K_el =np.zeros((mV*ndofV,mV*ndofV),dtype=np.float64)
G_el=np.zeros((mV*ndofV,mP*ndofP),dtype=np.float64)
h_el=np.zeros((mP*ndofP),dtype=np.float64)
for kq in range(0,nqel):
rq=qcoords_r[kq]
sq=qcoords_s[kq]
weightq=qweights[kq]
#compute coords of quadrature points
NNNV=NNN(rq,sq,mapping)
xq=np.dot(NNNV[:],xmapping[:,iel])
yq=np.dot(NNNV[:],zmapping[:,iel])
#zq[counterq]=yq
#radq[counterq]=np.sqrt(xq**2+yq**2)
#thetaq[counterq]=np.pi/2-np.arctan2(yq,xq)
#compute jacobian matrix
dNNNVdr=dNNNdr(rq,sq,mapping)
dNNNVds=dNNNds(rq,sq,mapping)
jcb[0,0]=np.dot(dNNNVdr[:],xmapping[:,iel])
jcb[0,1]=np.dot(dNNNVdr[:],zmapping[:,iel])
jcb[1,0]=np.dot(dNNNVds[:],xmapping[:,iel])
jcb[1,1]=np.dot(dNNNVds[:],zmapping[:,iel])
jcob=np.linalg.det(jcb)
jcbi=np.linalg.inv(jcb)
#basis functions
NNNV=NNN(rq,sq,'Q2')
dNNNVdr=dNNNdr(rq,sq,'Q2')
dNNNVds=dNNNds(rq,sq,'Q2')
NNNP=NNN(rq,sq,'Q1')
# compute dNdx & dNdy
for k in range(0,mV):
dNNNVdx[k]=jcbi[0,0]*dNNNVdr[k]+jcbi[0,1]*dNNNVds[k]
dNNNVdy[k]=jcbi[1,0]*dNNNVdr[k]+jcbi[1,1]*dNNNVds[k]
#end for
if axisymmetric: