def plotRelaxTimes():
rextime=[]
Wi = np.array([2,4,8,16,32,64,128])
for w in Wi:
mydict = mat2py.read(os.path.expanduser('~/rsyncfolder/data/VEflow/TwoHeadSpring/springtestC_visco%03d.mat' % w))
vals = np.zeros(mydict['S'].shape)
vals[:,:,:,0,0] = 1
vals[:,:,:,1,1] = 1
difs = np.abs(mydict['S'] - vals)
print(len(mydict['t'].flatten()))
for k in range(40,len(mydict['t'].flatten())):
if np.all(difs[k,:,:,:,:]<0.06):
rextime.append(mydict['t'].flatten()[k])
print((w,k))
break
if k == len(mydict['t'])-1:
print('no convergence for Wi = %f' % w)
mydict={}
print(rextime)
plt.close()
plt.plot(Wi/10.,np.asarray(rextime),'k',linewidth=4.0)
plt.tick_params(labelsize=24)
plt.title('Relaxation time vs Wi', fontsize=24)
plt.xlabel('Wi', fontsize=24)
plt.ylabel('Stress within 6% of I', fontsize=24)
plt.savefig(os.path.expanduser('~/rsyncfolder/data/VEflow/TwoHeadSpring/relaxtimes.pdf'))
def plotcomponents(fend='_nodegrid', fstart='swimmerC', tbegin=3):
if fend == '' or fend == '_centergrid':
fname1 = 'center_' + fstart + '_compratL2_'
fname2 = 'center_' + fstart + '_compL2_'
elif fend == '_nodegrid':
fname1 = 'node_' + fstart + '_compratL2_'
fname2 = 'node_' + fstart + '_compL2_'
elif fend == '_centergrid_lowerfish':
fname1 = 'lower_' + fstart + '_compratL2_'
fname2 = 'lower_' + fstart + '_compL2_'
for comp in [(0, 0), (0, 1), (1, 0), (1, 1)]:
comps = []
h = []
N = []
M = []
for k, j in enumerate(2**np.arange(4)):
mydict = mat2py.read(
os.path.expanduser('~/scratch/' + fstart + '_visco_nove%03d' %
(j * 20) + fend + '.mat'))
h.append(mydict['pdict']['gridspc'][0, 0])
N.append(mydict['pdict']['N'][0, 0])
M.append(mydict['pdict']['M'][0, 0])
print((h[k], N[k], M[k]))
times = mydict['t'].flatten()
ctemp = []
for t in range(len(times)):
gl = SD2D.vectorGrad(mydict['l'][t, :, :, :], h[k], N[k], M[k])
x = ((gl[:, :, comp[0], comp[1]])**2).sum()
l2measure = h[k] * np.sqrt(x)
ctemp.append(l2measure)
comps.append(ctemp)
comps = np.asarray(comps).transpose().squeeze()
Rats = np.zeros((comps.shape[0] - tbegin, 2))
plt.clf()
for i in [1]:
Rats[:, i] = (comps[tbegin:, i] - comps[tbegin:, i + 1]) / (
comps[tbegin:, i + 1] - comps[tbegin:, i + 2])
plt.plot(mydict['t'].flatten()[tbegin:], Rats[:, i])
print(np.max(Rats))
plt.title('Ratios for component %d%d ($L_2$ measure)' % comp)
plt.xlabel('Time')
plt.savefig(os.path.expanduser('~/scratch/' + fname1 + '%d%d' % comp))
plt.clf()
for i, k in enumerate(['$N=20$', '$N=40$', '$N=80$', '$N=160$']):
plt.plot(mydict['t'].flatten(), comps[:, i], label=k)
plt.title('Component %d%d ($L_2$ measure)' % comp)
plt.xlabel('Time')
plt.legend(loc=0)
plt.savefig(os.path.expanduser('~/scratch/' + fname2 + '%d%d' % comp))
print('done')
def plotdetl2error(fend='_nodegrid', fstart='swimmerC', tbegin=3):
if fend == '' or fend == '_centergrid':
fname1 = 'center_' + fstart + '_deterrratL2'
fname2 = 'center_' + fstart + '_deterrL2'
elif fend == '_nodegrid':
fname1 = 'node_' + fstart + '_deterrratL2'
fname2 = 'node_' + fstart + '_deterrL2'
elif fend == '_centergrid_lowerfish':
fname1 = 'lower_' + fstart + '_deterrratL2'
fname2 = 'lower_' + fstart + '_deterrL2'
dets = []
h = []
N = []
M = []
for k, j in enumerate(2**np.arange(4)):
mydict = mat2py.read(
os.path.expanduser('~/scratch/' + fstart + '_visco_nove%03d' %
(j * 20) + fend + '.mat'))
h.append(mydict['pdict']['gridspc'][0, 0])
N.append(mydict['pdict']['N'])
M.append(mydict['pdict']['M'])
times = mydict['t'].flatten()
ctemp = []
for t in range(len(times)):
x = ((mydict['alldets'][t, :, :] - 1)**2).sum()
l2measure = h[k] * np.sqrt(x)
ctemp.append(l2measure)
dets.append(ctemp)
dets = np.asarray(dets).squeeze().transpose()
Rats = np.zeros((dets.shape[0] - tbegin, 2))
plt.clf()
for i in [1]:
Rats[:, i] = (dets[tbegin:, i] - dets[tbegin:, i + 1]) / (
dets[tbegin:, i + 1] - dets[tbegin:, i + 2])
plt.plot(mydict['t'].flatten()[tbegin:], Rats[:, i])
print(np.max(Rats))
plt.title('Ratios for det $L_2$ error')
plt.xlabel('Time')
plt.savefig(os.path.expanduser('~/scratch/' + fname1))
plt.clf()
for i, k in enumerate(['$N=20$', '$N=40$', '$N=80$', '$N=160$']):
plt.plot(mydict['t'].flatten(), dets[:, i], label=k)
plt.title('Det $L_2$ error')
plt.xlabel('Time')
plt.legend(loc=0)
plt.savefig(os.path.expanduser('~/scratch/' + fname2))
print('done')
def pcolordet(fend='_nodegrid', fstart='swimmerC'):
plt.close()
fig = plt.figure()
for k, j in enumerate(2**np.arange(4)):
mydict = mat2py.read(
os.path.expanduser('~/scratch/' + fstart + '_visco_nove%03d' %
(j * 20) + fend + '.mat'))
fname = 'swimmerv_dets%03d_' % (j * 20) + fstart + '_' + fend + '_'
vmin = np.min(mydict['alldets'])
vmax = np.max(mydict['alldets'])
x = mydict['l'][:, :, :, 0]
y = mydict['l'][:, :, :, 1]
xmin = np.min(x)
xmax = np.max(x)
ymin = np.min(y)
ymax = np.max(y)
sx = mydict['fpts'][:, :-1:2]
sy = mydict['fpts'][:, 1::2]
c = 0
for t in range(len(mydict['t'].flatten())):
# vmin=np.min(mydict['alldets'][t,:,:])
# vmax=np.max(mydict['alldets'][t,:,:])
plt.pcolor(x[t, :, :],
y[t, :, :],
mydict['alldets'][t, :, :],
vmin=vmin,
vmax=vmax,
cmap='jet')
plt.colorbar()
if len(sx[t, :]) > 1:
plt.plot(sx[t, :], sy[t, :], 'k', linewidth=4.0)
else:
plt.plot(sx[t, :], sy[t, :], 'k.', markersize=16.0)
plt.title('Time = ' + str(mydict['t'][0, t]))
plt.savefig(os.path.expanduser('~/scratch/' + fname + '%03d' % c))
c += 1
plt.clf()
plt.close()
def read(self, stream, filetype, **kw):
d = mat2py.read(stream)
return (gicdat.doc.Doc(d), None)
def plotMaxMinDiv(fend='_nodegrid', fstart='swimmerC', tbegin=6):
if fend == '' or fend == '_centergrid':
fname1 = 'center_' + fstart + '_maxdiv'
fname2 = 'center_' + fstart + '_mindiv'
elif fend == '_nodegrid':
fname1 = 'node_' + fstart + '_maxdiv'
fname2 = 'node_' + fstart + '_mindiv'
elif fend == '_centergrid_lowerfish':
fname1 = 'lower_' + fstart + '_maxdiv'
fname2 = 'lower_' + fstart + '_mindiv'
maxdiv = []
mindiv = []
N = []
M = []
for k, j in enumerate(2**np.arange(4)):
mydict = mat2py.read(
os.path.expanduser('~/scratch/' + fstart + '_visco_nove%03d' %
(j * 20) + fend + '.mat'))
N.append(mydict['pdict']['N'])
M.append(mydict['pdict']['M'])
times = mydict['t'].flatten()
x = mydict['l'][:, :, :, 0]
y = mydict['l'][:, :, :, 1]
dt = mydict['dt'].flatten()
h = mydict['pdict']['gridspc'].flatten()
ctemp = []
ctemp1 = []
Mv = np.zeros(mydict['l'][0, :, :, :].shape)
for t in range(1, len(times) - 1):
u = (x[t + 1, :, :] - x[t - 1, :, :]) / (
2 * dt) #center difference approximation to velocity
v = (y[t + 1, :, :] - y[t - 1, :, :]) / (2 * dt)
Mv[:, :, 0] = u
Mv[:, :, 1] = v
gM = SD2D.vectorGrad(
Mv, h, N[k], M[k]) # du/da (Lagrangian derivative of velocity)
gMs = np.reshape(gM, (N[k] * M[k], 2, 2))
gl = SD2D.vectorGrad(mydict['l'][t, :, :, :], h, N[k],
M[k]) # F (Jacobian matrix)
gls = np.reshape(gl, (N[k] * M[k], 2, 2))
igls = cm.matinv2x2(gls) #inverse Jacobian matrix
div = []
for i in range(N[k] * M[k]):
gradu = np.dot(
gMs[i, :, :], igls[i, :, :]
) # du/dx = (du/da)F^{-1} (Eularian derivative of vel is transform of Lagrangian)
div.append(gradu[0, 0] + gradu[1, 1]) # div(u) = trace(du/dx)
ctemp.append(np.max(div))
ctemp1.append(np.min(div))
maxdiv.append(ctemp)
mindiv.append(ctemp1)
maxdiv = np.asarray(maxdiv).squeeze().transpose()
mindiv = np.asarray(mindiv).squeeze().transpose()
plt.clf()
for i, k in enumerate(['$N=20$', '$N=40$', '$N=80$', '$N=160$']):
plt.plot(times[1:-1], maxdiv[:, i], label=k)
plt.title('Max Div')
plt.xlabel('Time')
plt.legend(loc=0)
plt.savefig(os.path.expanduser('~/scratch/' + fname1))
plt.clf()
for i, k in enumerate(['$N=20$', '$N=40$', '$N=80$', '$N=160$']):
plt.plot(times[1:-1], mindiv[:, i], label=k)
plt.title('Min Div')
plt.xlabel('Time')
plt.legend(loc=0)
plt.savefig(os.path.expanduser('~/scratch/' + fname2))
print('done')
def plotDiv(fend='_nodegrid', fstart='swimmerC', tbegin=6):
if fend == '' or fend == '_centergrid':
fname1 = 'center_' + fstart + '_divratL2'
fname2 = 'center_' + fstart + '_divL2'
fname3 = 'center_' + fstart + '_divratL1'
fname4 = 'center_' + fstart + '_divL1'
elif fend == '_nodegrid':
fname1 = 'node_' + fstart + '_divratL2'
fname2 = 'node_' + fstart + '_divL2'
fname3 = 'node_' + fstart + '_divratL1'
fname4 = 'node_' + fstart + '_divL1'
elif fend == '_centergrid_lowerfish':
fname1 = 'lower_' + fstart + '_divratL2'
fname2 = 'lower_' + fstart + '_divL2'
fname3 = 'lower_' + fstart + '_divratL1'
fname4 = 'lower_' + fstart + '_divL1'
divl2 = []
divl1 = []
N = []
M = []
for k, j in enumerate(2**np.arange(4)):
mydict = mat2py.read(
os.path.expanduser('~/scratch/' + fstart + '_visco_nove%03d' %
(j * 20) + fend + '.mat'))
N.append(mydict['pdict']['N'])
M.append(mydict['pdict']['M'])
times = mydict['t'].flatten()
x = mydict['l'][:, :, :, 0]
y = mydict['l'][:, :, :, 1]
dt = mydict['dt'].flatten()
h = mydict['pdict']['gridspc'].flatten()
ctemp = []
ctemp1 = []
Mv = np.zeros(mydict['l'][0, :, :, :].shape)
for t in range(1, len(times) - 1):
u = (x[t + 1, :, :] - x[t - 1, :, :]) / (
2 * dt) #center difference approximation to velocity
v = (y[t + 1, :, :] - y[t - 1, :, :]) / (2 * dt)
Mv[:, :, 0] = u
Mv[:, :, 1] = v
gM = SD2D.vectorGrad(
Mv, h, N[k], M[k]) # du/da (Lagrangian derivative of velocity)
gMs = np.reshape(gM, (N[k] * M[k], 2, 2))
gl = SD2D.vectorGrad(mydict['l'][t, :, :, :], h, N[k],
M[k]) # F (Jacobian matrix)
gls = np.reshape(gl, (N[k] * M[k], 2, 2))
igls = cm.matinv2x2(gls) #inverse Jacobian matrix
div = []
for i in range(N[k] * M[k]):
gradu = np.dot(
gMs[i, :, :], igls[i, :, :]
) # du/dx = (du/da)F^{-1} (Eularian derivative of vel is transform of Lagrangian)
div.append(gradu[0, 0] + gradu[1, 1]) # div(u) = trace(du/dx)
l2measure = h * np.sqrt((np.asarray(div)**2).sum())
l1measure = h**2 * (np.abs(np.asarray(div))).sum()
ctemp.append(l2measure)
ctemp1.append(l1measure)
divl2.append(ctemp)
divl1.append(ctemp1)
divl2 = np.asarray(divl2).squeeze().transpose()
Rats = np.zeros((divl2.shape[0] - tbegin + 1, 2))
plt.clf()
for i in [0]:
Rats[:,
i] = (divl2[(tbegin - 1):, i] - divl2[(tbegin - 1):, i + 1]) / (
divl2[(tbegin - 1):, i + 1] - divl2[(tbegin - 1):, i + 2])
plt.plot(times[tbegin:-1], Rats[:, i])
print(np.max(Rats))
plt.title('Ratios for divergence $L_2$')
plt.xlabel('Time')
plt.savefig(os.path.expanduser('~/scratch/' + fname1))
plt.clf()
for i, k in enumerate(['$N=20$', '$N=40$', '$N=80$', '$N=160$']):
plt.plot(times[1:-1], divl2[:, i], label=k)
plt.title('Div $L_2$')
plt.xlabel('Time')
plt.legend(loc=0)
plt.savefig(os.path.expanduser('~/scratch/' + fname2))
divl1 = np.asarray(divl1).squeeze().transpose()
Rats1 = np.zeros((divl1.shape[0] - tbegin + 1, 2))
plt.clf()
for i in [0]:
Rats[:,
i] = (divl1[(tbegin - 1):, i] - divl1[(tbegin - 1):, i + 1]) / (
divl1[(tbegin - 1):, i + 1] - divl1[(tbegin - 1):, i + 2])
plt.plot(times[tbegin:-1], Rats[:, i])
print(np.max(Rats))
plt.title('Ratios for divergence $L_1$')
plt.xlabel('Time')
plt.savefig(os.path.expanduser('~/scratch/' + fname3))
plt.clf()
for i, k in enumerate(['$N=20$', '$N=40$', '$N=80$', '$N=160$']):
plt.plot(times[1:-1], divl1[:, i], label=k)
plt.title('Div $L_1$')
plt.xlabel('Time')
plt.legend(loc=0)
plt.savefig(os.path.expanduser('~/scratch/' + fname4))
print('done')