def viscoElasticUpdater_bgvel(t, y, wdict):
#interior function for incompressible background flow only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
pdict = wdict['pdict']
N = pdict['N']
M = pdict['M']
l2 = np.reshape(y[range(2 * N * M)], (N * M, 2))
l3 = np.reshape(l2, (N, M, 2))
P2 = np.reshape(y[(2 * N * M):], (N * M, 2, 2))
P3 = np.reshape(P2, (N, M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P3, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3, pdict['gridspc'], N, M)
F = np.reshape(F, (N * M, 2, 2))
#calculate new velocities at all points of interest
ub, gradub = wdict['myVelocity'](pdict, l2)
lt0 = pdict['gridspc']**2 * CM.matmult(pdict['eps_grid'], pdict['mu'], l2,
l2, Pd)
# reshape the velocities on the grid
lt3 = np.reshape(lt0, (N, M, 2))
lt = ub + lt0
# calculate new stress time derivatives
gradlt = SD2D.vectorGrad(lt3, pdict['gridspc'], N, M)
gradlt = np.reshape(gradlt, (N * M, 2, 2))
Pt = CM.stressDeriv(pdict['Wi'], gradub, gradlt, F, P2)
# gradlt = pdict['gridspc']**2*CM.derivop(pdict['eps_grid'],pdict['mu'],l2,l2,Pd,F) #grad(Stokeslet) method
# Finv = CM.matinv2x2(F) #first grad(u) method
# Pt = np.zeros((N*M,2,2)) #first grad(u) method
# for j in range(N*M):
# Pt[j,:,:] = np.dot(gradub[j,:,:],P2[j,:,:]) + np.dot(np.dot(gradlt[j,:,:],Finv[j,:,:]),P2[j,:,:]) - (1./pdict['Wi'])*(P2[j,:,:] - Finv[j,:,:].transpose())
return np.append(lt, Pt.flatten())
def calcState_dets(r,t0,regridding,regriddict,alldetflag=1):
regridflag = False
addptsflag = False
StateNow = {}
StateNow['t'] = r.t
wdict = r.f_params[0]
pdict=wdict['pdict']
try:
N = pdict['N']
M = pdict['M']
except:
N = 0
M = 0
Q = len(r.y) - 2*N*M - 4*N*M
adarray=np.zeros((N,M))
if N == 0: #stokes flow without markers
StateNow['fpts']=r.y
elif Q < 0: #stokes flow with markers
StateNow['fpts']=r.y[:2*N*M]
l3D = np.reshape(r.y[-2*N*M:],(N,M,2))
StateNow['l']=l3D
if alldetflag:
F = SD2D.vectorGrad(l3D,pdict['gridspc'],N,M)
for j in range(N):
for k in range(M):
Fs = F[j,k,:,:]
gdet = np.linalg.det(Fs)
adarray[j,k] = gdet
StateNow['alldets']=adarray
elif Q >= 0: #viscoelastic flow
StateNow['fpts']=r.y[:Q]
l3D = np.reshape(r.y[range(Q,Q+2*N*M)],(N,M,2))
StateNow['l']=l3D
F = SD2D.vectorGrad(l3D,pdict['gridspc'],N,M)
Ptemp = np.reshape(r.y[(Q+2*N*M):],(N,M,2,2))
Stemp = np.zeros((N,M,2,2))
tr = np.zeros((N,M))
for j in range(N):
for k in range(M):
Fs = F[j,k,:,:]
if alldetflag or (regriddict['detcrit'] != None):
gdet = np.linalg.det(Fs)
adarray[j,k] = gdet
Ps = Ptemp[j,k,:,:]
Stemp[j,k,:,:]=np.dot(Ps,Fs.transpose())
tr[j,k] = Stemp[j,k,0,0] + Stemp[j,k,1,1]
StateNow['S']=Stemp
StateNow['Strace']=tr
if alldetflag:
StateNow['alldets']=adarray
if regridding:
if regriddict['timecrit'] != None:
regridflag, addptsflag = regridFlagFixedTime(r.t,t0,regriddict['timecrit'],regriddict['addpts'])
elif regriddict['edgecrit'] != None:
regridflag, addptsflag = regridFlagAdaptiveCloseToEdge(tr,N,M,regriddict['edgecrit'],regriddict['addpts'])
elif regriddict['detcrit'] != None:
regridflag, addptsflag = regridFlagAdaptiveDistortedDet(adarray,regriddict['detcrit'],regriddict['addpts'])
else:
print('Warning: No regridding algorithm specified. Regridding ignored.')
return StateNow, regridflag, addptsflag
def viscoElasticUpdater_bgvel(t,y,wdict):
#interior function for incompressible background flow only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
pdict = wdict['pdict']
N = pdict['N']
M = pdict['M']
l2 = np.reshape(y[range(2*N*M)],(N*M,2))
l3 = np.reshape(l2,(N,M,2))
P2 = np.reshape(y[(2*N*M):],(N*M,2,2))
P3 = np.reshape(P2,(N,M,2,2))
#calculate tensor derivative
Pd = pdict['beta']*SD2D.tensorDiv(P3,pdict['gridspc'],N,M)
Pd = np.reshape(Pd,(N*M,2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3,pdict['gridspc'],N,M)
F = np.reshape(F,(N*M,2,2))
#calculate new velocities at all points of interest
ub, gradub = wdict['myVelocity'](pdict,l2)
lt0 = pdict['gridspc']**2*CM.matmult(pdict['eps_grid'],pdict['mu'],l2,l2,Pd)
# reshape the velocities on the grid
lt3 = np.reshape(lt0,(N,M,2))
lt = ub + lt0
# calculate new stress time derivatives
gradlt = SD2D.vectorGrad(lt3,pdict['gridspc'],N,M)
gradlt = np.reshape(gradlt,(N*M,2,2))
Pt = CM.stressDeriv(pdict['Wi'],gradub,gradlt,F,P2)
# gradlt = pdict['gridspc']**2*CM.derivop(pdict['eps_grid'],pdict['mu'],l2,l2,Pd,F) #grad(Stokeslet) method
# Finv = CM.matinv2x2(F) #first grad(u) method
# Pt = np.zeros((N*M,2,2)) #first grad(u) method
# for j in range(N*M):
# Pt[j,:,:] = np.dot(gradub[j,:,:],P2[j,:,:]) + np.dot(np.dot(gradlt[j,:,:],Finv[j,:,:]),P2[j,:,:]) - (1./pdict['Wi'])*(P2[j,:,:] - Finv[j,:,:].transpose())
return np.append(lt,Pt.flatten())
def simresults(basename, basedir):
'''Retrieve approximate solution from saved output'''
mydict = fileops.loadPickle(basename=basename, basedir=basedir)
l = mydict['l']
S = mydict['S']
F = []
Finv = []
P = []
N = l[0].shape[0]
M = l[0].shape[1]
for k in range(len(mydict['t'])):
Ft = SD2D.vectorGrad(l[k], mydict['pdict']['gridspc'], N, M)
Ftemp = np.reshape(Ft, (N * M, 2, 2))
Ftinv = CM.matinv2x2(Ftemp)
Ftinv = np.reshape(Ftinv, (N, M, 2, 2))
F.append(Ft.copy())
Finv.append(Ftinv.copy())
stress = np.zeros((N, M, 2, 2))
for j in range(N):
for m in range(M):
stress[j,
m, :, :] = S[k][j,
m, :, :] * Ftinv[j,
m, :, :].transpose()
P.append(stress.copy())
return l, P, S, F, Finv, mydict
def viscoElasticUpdater_force(t, y, wdict):
#interior function for force pts only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
pdict = wdict['pdict']
pdict['forcedict']['t'] = t
N = pdict['N']
M = pdict['M']
Q = len(y) / 2 - N * M - 2 * N * M
fpts = np.reshape(y[:2 * Q], (Q, 2))
l2 = np.reshape(y[range(2 * Q, 2 * Q + 2 * N * M)], (N * M, 2))
l3 = np.reshape(l2, (N, M, 2))
allpts = np.reshape(
y[:2 * Q + 2 * N * M],
(Q + N * M, 2)) # both force points and Lagrangian points
P2 = np.reshape(y[(2 * Q + 2 * N * M):], (N * M, 2, 2))
P3 = np.reshape(P2, (N, M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P3, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate spring forces
f = wdict['myForces'](fpts, **pdict['forcedict'])
#calculate new velocities at all points of interest (Lagrangian points and force points)
lt = pdict['gridspc']**2 * CM.matmult(
pdict['eps_grid'], pdict['mu'], allpts, l2, Pd) + CM.matmult(
pdict['eps_obj'], pdict['mu'], allpts, fpts, f)
# reshape the velocities on the grid
lt3 = np.reshape(lt[2 * Q:], (N, M, 2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3, pdict['gridspc'], N, M)
F = np.reshape(F, (N * M, 2, 2))
#calculate new stress time derivatives
# gradlt = pdict['gridspc']**2*CM.derivop(pdict['eps_grid'],pdict['mu'],l2,l2,Pd,F) + CM.derivop(pdict['eps_obj'],pdict['mu'],l2,fpts,f,F) #grad(Stokeslet) method
gradlt = SD2D.vectorGrad(lt3, pdict['gridspc'], N, M)
gradlt = np.reshape(gradlt, (N * M, 2, 2))
gradub = np.zeros(gradlt.shape)
# Finv = CM.matinv2x2(F) # first grad(u) method
# Pt = np.zeros((N*M,2,2))
# for j in range(N*M):
# Pt[j,:,:] = np.dot(np.dot(gradlt[j,:,:],Finv[j,:,:]),P2[j,:,:]) - (1./pdict['Wi'])*(P2[j,:,:] - Finv[j,:,:].transpose())
Pt = CM.stressDeriv(pdict['Wi'], gradub, gradlt, F, P2)
return np.append(lt, Pt.flatten())
def viscoElasticUpdater_force(t,y,wdict):
#interior function for force pts only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
pdict = wdict['pdict']
pdict['forcedict']['t'] = t
N = pdict['N']
M = pdict['M']
Q = len(y)/2 - N*M - 2*N*M
fpts = np.reshape(y[:2*Q],(Q,2))
l2 = np.reshape(y[range(2*Q,2*Q+2*N*M)],(N*M,2))
l3 = np.reshape(l2,(N,M,2))
allpts = np.reshape(y[:2*Q+2*N*M],(Q+N*M,2)) # both force points and Lagrangian points
P2 = np.reshape(y[(2*Q+2*N*M):],(N*M,2,2))
P3 = np.reshape(P2,(N,M,2,2))
#calculate tensor derivative
Pd = pdict['beta']*SD2D.tensorDiv(P3,pdict['gridspc'],N,M)
Pd = np.reshape(Pd,(N*M,2))
#calculate spring forces
f = wdict['myForces'](fpts,**pdict['forcedict'])
#calculate new velocities at all points of interest (Lagrangian points and force points)
lt = pdict['gridspc']**2*CM.matmult(pdict['eps_grid'],pdict['mu'],allpts,l2,Pd) + CM.matmult(pdict['eps_obj'],pdict['mu'],allpts,fpts,f)
# reshape the velocities on the grid
lt3 = np.reshape(lt[2*Q:],(N,M,2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3,pdict['gridspc'],N,M)
F = np.reshape(F,(N*M,2,2))
#calculate new stress time derivatives
# gradlt = pdict['gridspc']**2*CM.derivop(pdict['eps_grid'],pdict['mu'],l2,l2,Pd,F) + CM.derivop(pdict['eps_obj'],pdict['mu'],l2,fpts,f,F) #grad(Stokeslet) method
gradlt = SD2D.vectorGrad(lt3,pdict['gridspc'],N,M)
gradlt = np.reshape(gradlt,(N*M,2,2))
gradub = np.zeros(gradlt.shape)
# Finv = CM.matinv2x2(F) # first grad(u) method
# Pt = np.zeros((N*M,2,2))
# for j in range(N*M):
# Pt[j,:,:] = np.dot(np.dot(gradlt[j,:,:],Finv[j,:,:]),P2[j,:,:]) - (1./pdict['Wi'])*(P2[j,:,:] - Finv[j,:,:].transpose())
Pt = CM.stressDeriv(pdict['Wi'],gradub,gradlt,F,P2)
return np.append(lt,Pt.flatten())
def calcState_nodets(r, t0, regridding, regriddict, alldetflag=0):
regridflag = False
addptsflag = False
StateNow = {}
StateNow['t'] = r.t
wdict = r.f_params[0]
pdict = wdict['pdict']
try:
N = pdict['N']
M = pdict['M']
except:
N = 0
M = 0
Q = len(r.y) - 2 * N * M - 4 * N * M
if N == 0: #stokes flow without markers
StateNow['fpts'] = r.y
elif Q < 0: #stokes flow with markers
StateNow['fpts'] = r.y[:2 * N * M]
l3D = np.reshape(r.y[-2 * N * M:], (N, M, 2))
StateNow['l'] = l3D
elif Q >= 0: #viscoelastic flow
StateNow['fpts'] = r.y[:Q]
l3D = np.reshape(r.y[range(Q, Q + 2 * N * M)], (N, M, 2))
StateNow['l'] = l3D
F = SD2D.vectorGrad(l3D, pdict['gridspc'], N, M)
Ptemp = np.reshape(r.y[(Q + 2 * N * M):], (N, M, 2, 2))
Stemp = np.zeros((N, M, 2, 2))
tr = np.zeros((N, M))
for j in range(N):
for k in range(M):
Fs = F[j, k, :, :]
Ps = Ptemp[j, k, :, :]
Stemp[j, k, :, :] = np.dot(Ps, Fs.transpose())
tr[j, k] = Stemp[j, k, 0, 0] + Stemp[j, k, 1, 1]
StateNow['S'] = Stemp
StateNow['Strace'] = tr
if regridding:
if regriddict['timecrit'] != None:
regridflag, addptsflag = regridFlagFixedTime(
r.t, t0, regriddict['timecrit'], regriddict['addpts'])
elif regriddict['edgecrit'] != None:
regridflag, addptsflag = regridFlagAdaptiveCloseToEdge(
tr, N, M, regriddict['edgecrit'], regriddict['addpts'])
else:
print(
'Warning: No regridding algorithm specified. Regridding ignored.'
)
return StateNow, regridflag, addptsflag
def simresults(basename, basedir):
'''Retrieve approximate solution from saved output'''
mydict = fileops.loadPickle(basename=basename, basedir=basedir)
l = mydict['l']
S=mydict['S']
F=[]
Finv=[]
P=[]
N = l[0].shape[0]
M = l[0].shape[1]
for k in range(len(mydict['t'])):
Ft = SD2D.vectorGrad(l[k],mydict['pdict']['gridspc'],N,M)
Ftemp = np.reshape(Ft,(N*M,2,2))
Ftinv = CM.matinv2x2(Ftemp)
Ftinv = np.reshape(Ftinv,(N,M,2,2))
F.append(Ft.copy())
Finv.append(Ftinv.copy())
stress = np.zeros((N,M,2,2))
for j in range(N):
for m in range(M):
stress[j,m,:,:] = S[k][j,m,:,:]*Ftinv[j,m,:,:].transpose()
P.append(stress.copy())
return l, P, S, F, Finv, mydict
