def scenario3pts():
l = 1.e-5
U = np.array([6.e-5, 4.5e-5, 5.e-5])
mu = 1.e-3
eps = [l / 2., 3 * l / 2.]
v = -1 * np.array([[
np.cos(np.pi / 6), np.sin(np.pi / 6), 0
], [np.cos(5 * np.pi / 6), np.sin(5 * np.pi / 6), 0
], [np.cos(-np.pi / 2), np.sin(-np.pi / 2), 0]])
xh = -4.e-6 * v
x = np.arange(-1.e-3, 1.01e-3, 1.e-5)
X, Y = np.meshgrid(x, x)
xu = np.column_stack([
np.column_stack([X.flatten(), Y.flatten()]),
np.zeros(X.flatten().shape)
])
u, xt = calcFlow(xu, xh, v, U, l, eps, mu)
yu = xu[:, 1].reshape((len(x), len(x)))
xu = xu[:, 0].reshape((len(x), len(x)))
v = u[:, 1].reshape((len(x), len(x)))
u = u[:, 0].reshape((len(x), len(x)))
# plotVels(xu,yu,u,v,xh,xt)
mat2py.write('/Users/bcummins/colonyvel.mat', {
'xu': xu,
'yu': yu,
'xh': xh,
'xt': xt,
'u': u,
'v': v,
'eps': eps
})
return xu, yu, u, v, xh, xt
def write(self, d, stream, filetype, **kw):
'''
d is a dictionary of gicdat.doc.Node instances, of the sort returned by
gicdat.Doc.allNodes(). Stream is a file-like object open in write mode.
filetype is a mime-type-like string. kw args are implementation
specific
Write should return None
'''
mat2py.write(stream, d)
def mySwimmer():
#get ready to save files
import mat2py
import os
#dictionary of variables for both Stokes flow and viscoelastic flow
pdict = dict(N=40, M=16, gridspc=1.5 / 40, origin=[0, 0], mu=1, Wi=0.2)
pdict['beta'] = 1. / (2 * pdict['Wi'])
#set time parameters, save data every numskip time steps
t0 = 0
totalTime = 1
dt = 1.e-4
numskip = 500
#save file name
fname = os.path.expanduser('~/scratch/swimmer')
#make swimmer
#first assign params
a = 0.1
w = 2 * np.pi
lam = 8.4 #2*np.pi/0.75
Np = 20
L = 0.78
h = L / (Np - 1)
pdict['K'] = 100
pdict['xr'] = np.array([h])
pdict['forcedict'] = {'a': a, 'w': w, 't': 0, 'Kcurv': 0.25, 'lam': lam}
pdict['eps'] = 0.75 * h
#Now setup initial conditions
y0 = 0.3 * np.ones((2 * Np, ))
v = np.arange(0.5, 0.5 + L + h / 2, h)
y0[:-1:2] = v #initial conds [x0,y0,x1,y1,...,xn,yn]
#add unsaveable entries
pdict1 = pdict.copy()
pdict1['myForces'] = calcForcesSwimmer
pdict1['blob'] = RS2D.CubicRegStokeslet(pdict['eps'], pdict['mu'])
pdict1['blobderiv'] = RS2D.CubicRegStokesletDeriv(pdict['eps'],
pdict['mu'])
#run the ode solver
print('Stokes flow...')
fpts, t, l, S, Strace = mySolver(stokesFlowUpdater, y0, t0, dt, totalTime,
'bdf', pdict1, numskip)
mat2py.write(fname + '_stokes_RicardoParams_08162011.mat', {
't': t,
'fpts': fpts,
'pdict': pdict,
'dt': dt
})
if quadtype == 't':
quad = qm.CompTrapRule(circ.quadspacing)
print('Trapezoid Rule')
elif quadtype == 's':
quad = qm.CompSimpRule(circ.quadspacing)
print("Simpson's Rule")
elif quadtype == 'r':
quad = qm.RiemannSum(circ.quadspacing)
print('Riemann Sum')
if basistype == 'c':
basfun = CstBasisFunc(M, quadtype)
print(basfun.phi)
elif basistype == 'h':
basfun = HatBasisFunc(M, quadtype)
print(basfun.phi)
P = basfun.phi.shape[0]
coeffs = quad.makeCoeffs(P)
subintegral = nm.sum(coeffs * basfun.phi)
wholeintegral = nm.sum(f * subintegral)
print(wholeintegral)
data.append(wholeintegral)
data = nm.asarray(data)
exactans = (4 * nm.pi**3) / 3.
import mat2py as mf
mf.write('/Users/bcummins/basistest.mat', {
'N': numchords,
'intvals': data,
'exactans': exactans
})
print('Exact answer is ' + str(exactans))
origforcemat = origblob.makeMatrix2DOriginal(nodes,nodes)
origforces = useGMRES(origforcemat,BCs)
origvelmat = blob.makeMatrix2DOriginal(obspts,nodes)
origvel = nm.dot(origvelmat,origforces)
if len(u) == 0:
u = vel[0::2]
v = vel[1::2]
origu = origvel[0::2]
origv = origvel[1::2]
else:
u = nm.append(u,vel[0::2])
v = nm.append(v,vel[1::2])
origu = nm.append(origu,origvel[0::2])
origv = nm.append(origv,origvel[1::2])
fname = 'StokesCylTest_exactintegralsANDorig_points_singleblobfortable_N'+ (4-len(str(N)))*'0' + str(N) + '.mat'
mf.write(fname,{'u':u,'v':v,'origu':origu,'origv':origv,'exactu':exactu,'exactv':exactv,'obspts':obspts,'origbps':origblobparams,'eintbps':eintblobparams})
# #single blob for table, patches
# mu = 1.0
# rad = 0.25
# obspts = constructpatches()
# exactu, exactv = exactSoln(obspts,rad,mu)
# numchords = [2**k for k in range(3,9)]
# for N in numchords:
# nodes = discretizeCircle(N,rad)
# BCs = nm.asarray(N*[1,0])
# origblobparams = [2*nm.pi/(5*N)]
# eintblobparams = [(2*nm.pi/(5*N))**2]
# u = nm.empty((0,))
def mySprings():
#get ready to save files
import mat2py
#dictionary of variables for both Stokes flow and viscoelastic flow
pdictsave = dict(N=20,
M=20,
gridspc=1. / 20,
origin=[0.0, 0.0],
mu=1.0,
K=5.0,
xr=np.array([0.1]))
pdictsave['eps'] = 4 * pdictsave['gridspc']
pdict = pdictsave.copy()
pdict['myForces'] = calcForcesTwoHeadSpring
#set time parameters, save data every numskip time steps
t0 = 0
totalTime = 4
dt = 1.e-3
numskip = 50
#save file name
fname = os.path.expanduser('~/scratch/springtestC')
#Stokes flow test, works
print('Stokes flow...')
#set up initial conditions
y0 = np.array([0.3, 0.5, 0.7, 0.5])
#run the ode solver
fpts, t, l, S, Strace, alldets = mySolver(stokesFlowUpdater, y0, t0, dt,
totalTime, pdict, 'bdf', numskip)
#save the output
mat2py.write(fname + '_stokes.mat', {
't': t,
'fpts': fpts,
'pdict': pdictsave,
'dt': dt
})
#use same initial conditions for spring as in Stokes flow, but add on Lagrangian points and stress
N = pdict['N']
M = pdict['M']
gridspc = pdict['gridspc']
l0 = mygrids.makeGridCenter(N, M, gridspc, pdict['origin'])
P0 = np.zeros((N, M, 2, 2))
P0[:, :, 0, 0] = 1
P0[:, :, 1, 1] = 1
y0 = np.append(np.append(y0, l0.flatten()), P0.flatten())
for Wi in [0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8]:
print('Wi = %f' % Wi)
pdictsave['Wi'] = Wi
pdictsave['beta'] = 1. / (2 * Wi)
pdict['Wi'] = Wi
pdict['beta'] = 1. / (2 * Wi)
totalTime = 8 * np.ceil(Wi)
#Viscoelastic run
print('VE flow...')
#run the ode solver
fpts, t, l, S, Strace, alldets = mySolver(
viscoElasticUpdaterKernelDeriv, y0, t0, dt, totalTime, pdict,
'bdf', numskip)
#save the output
mat2py.write(
fname + '_visco%03d.mat' % int(Wi * 10), {
't': np.asarray(t),
'fpts': np.asarray(fpts),
'l': np.asarray(l),
'S': np.asarray(S),
'Strace': np.asarray(Strace),
'pdict': pdictsave,
'dt': dt
})
def mySpot():
#get ready to save files
import mat2py
import os
#dictionary of variables for both Stokes flow and viscoelastic flow
for N in [20, 40, 80, 160]:
pdict = dict(N=N,
M=(16 * N) / 40,
gridspc=1.5 / N,
origin=[0.0, 0.0],
mu=1.0,
Wi=0.2)
pdict['beta'] = 1. / (2 * pdict['Wi'])
#set time parameters, save data every time step
#note that I do not control the time step in the solver!!
# my time step only tells me where I will save data
t0 = 0
totalTime = 1.0
dt = 5.e-2
#save file name
fname = os.path.expanduser('~/scratch/spotC')
#make swimmer
#first assign params
Np = 20
L = 0.78
h = L / (Np - 1)
pdict['K'] = 10.0
pdict['xr'] = np.array([[1.173, 1.173]])
pdict['eps'] = 2 * (0.75 * h)
#Now setup initial conditions
y0 = np.array([0.8 - h / 2., 0.3 + h / 4.])
#add unsaveable entries
pdict1 = pdict.copy()
pdict1['myForces'] = calcForcesConstant
# #run the ode solver
# print('Stokes flow...')
# fpts, t, l, S, Strace = mySolver(stokesFlowUpdater,y0,t0,dt,totalTime,pdict1)
# mat2py.write(fname+'_stokesonly.mat', {'t':t,'fpts':fpts,'pdict':pdict,'dt':dt})
initTime = 0.0 #remove this when initialization in Stokes flow is desired
#make the grid
N = pdict['N']
M = pdict['M']
gridspc = pdict['gridspc']
l0 = mygrids.makeGridCenter(N, M, gridspc, pdict['origin'])
P0 = np.zeros((N, M, 2, 2))
# P0[:,:,0,0] = 1.0
# P0[:,:,1,1] = 1.0
y0 = np.append(np.append(y0, l0.flatten()), P0.flatten())
#Viscoelastic run
print('VE flow...')
fpts, t, l, S, Strace, alldets = mySolver(
viscoElasticUpdaterKernelDeriv, y0, initTime, dt,
totalTime + initTime, pdict1)
#save the output
mat2py.write(
fname + '_visco_nove%03d_centergrid.mat' % N, {
't': np.asarray(t),
'fpts': np.asarray(fpts),
'l': np.asarray(l),
'S': np.asarray(S),
'Strace': np.asarray(Strace),
'pdict': pdict,
'dt': dt,
'alldets': np.asarray(alldets)
})
def fallingStar():
########################################################
#falling star for art show
########################################################
#get ready to save files
import mat2py
#dictionary of variables
pdictsave = dict(N=80,
M=80,
gridspc=1. / 100,
origin=[0, 0],
mu=1.0,
K=0.05,
xr=[],
Wi=1.0)
pdictsave['beta'] = 1. / (2 * pdictsave['Wi'])
pdictsave['eps'] = 4 * pdictsave['gridspc']
pdict = pdictsave.copy()
pdict['myForces'] = calcForcesGravity
N = pdict['N']
M = pdict['M']
gridspc = pdict['gridspc']
#set time parameters
t0 = 0
totalTime = 0.45
dt = 1.e-2
numskip = 1
#save file name
fname = 'scratch/star_tree2C'
#make the star
R = 0.05
d = 0.05
r = 0.03
spc = 2 * np.pi / 16
theta = np.arange(0, 6 * np.pi + spc, spc)
x = (R - r) * np.cos(theta) + d * np.cos(theta * (R - r) / r) + 0.35
y = (R - r) * np.sin(theta) - d * np.sin(theta * (R - r) / r) + 0.45
fpts = np.column_stack([x, y])
pdictsave['n'] = fpts.shape[0]
pdict['n'] = fpts.shape[0]
#make tree marker points
lx = np.arange(0, 0.8 + gridspc / 2, gridspc)
llinex = 0.4 - lx * np.cos(np.pi / 3)
lliney = 0.8 - lx * np.sin(np.pi / 3)
bllinex = np.arange(0, 0.35 + gridspc / 2, gridspc)
blliney = 0.1 * np.ones(bllinex.shape)
mx = np.append(llinex, bllinex)
my = np.append(lliney, blliney)
ltrunky = np.arange(0.1, -gridspc / 2, -gridspc)
ltrunkx = 0.35 * np.ones(ltrunky.shape)
mx = np.append(mx, ltrunkx)
my = np.append(my, ltrunky)
btrunkx = np.arange(0.35, 0.45 + gridspc / 2, gridspc)
btrunky = np.zeros(btrunkx.shape)
mx = np.append(mx, btrunkx)
my = np.append(my, btrunky)
rtrunky = np.arange(0, 0.1 + gridspc / 2, gridspc)
rtrunkx = 0.45 * np.ones(rtrunky.shape)
mx = np.append(mx, rtrunkx)
my = np.append(my, rtrunky)
brlinex = np.arange(0.45, 0.8 + gridspc / 2, gridspc)
brliney = blliney
mx = np.append(mx, brlinex)
my = np.append(my, brliney)
rx = lx[range(len(lx) - 1, -1, -1)]
rlinex = 0.4 + rx * np.cos(np.pi / 3)
rliney = 0.8 - rx * np.sin(np.pi / 3)
mx = np.append(mx, rlinex)
my = np.append(my, rliney)
mpts = np.column_stack([mx, my])
#make the grid and stress ICs
l0 = mygrids.makeGridCenter(N, M, gridspc, pdict['origin'])
P0 = np.zeros((N, M, 2, 2))
P0[:, :, 0, 0] = 1
P0[:, :, 1, 1] = 1
y0 = np.append(
np.append(np.append(fpts.flatten(), mpts.flatten()), l0.flatten()),
P0.flatten())
#run the ode solver
fpts, t, l, S, Strace = mySolver(viscoElasticUpdaterKernelDeriv, y0, t0,
dt, totalTime, 'bdf', pdict, numskip)
#save the output
mat2py.write(
fname + '_visco.mat', {
't': np.asarray(t),
'fpts': np.asarray(fpts),
'l': np.asarray(l),
'S': np.asarray(S),
'Strace': np.asarray(Strace),
'pdict': pdictsave,
'dt': dt
})
# sys.exit()
N=10
print('N = 10')
nodes = nm.column_stack([nm.linspace(-N*0.05,N*0.05,N), nm.zeros(N)])
dt=nodes.dtype
df = nm.column_stack([nm.zeros(N),nm.ones(N)])
RHS = df.flatten()
eps = 0.005
blob = CubicRegStokeslet(eps,1,nodes,nodes,'open') #to solve matrix equation, use nodes as both sets of points
Ao = blob.makeMatrixOriginal('trap')
fo = useGMRES(Ao,RHS)
blobeval = CubicRegStokeslet(eps,1,obspts,nodes,'open')
Ao2 = blobeval.makeMatrixOriginal('trap')
uo = nm.dot(Ao2,fo)
uo = nm.reshape(uo,(uo.shape[0]/2,2))
Aes = blob.makeMatrixExactIntegralsSlow()
fes = useGMRES(Aes,RHS)
Aes2 = blobeval.makeMatrixExactIntegralsSlow()
ues = nm.dot(Aes2,fes)
ue = nm.reshape(ues,(ues.shape[0]/2,2))
# print(Ao)
# print(fo)
# print(Aes)
# print(fes)
print( nm.max( nm.sum((uo - ue)**2,1) / nm.sum(ue**2,1)) )
print( nm.sum( nm.sum((uo - ue)**2,1) / nm.sum(ue**2,1)) )
import mat2py
mat2py.write('testopencurve.mat',{'obspts':obspts,'uo':uo,'ue':ue})
#save file name
fname = 'scratch/oldversion_twohead'
#Stokes flow test, works
print('Stokes flow...')
#set up initial conditions
margin = (N * gridspc - 0.2) / 2
y0 = nm.array(
[margin, M * gridspc / 2, N * gridspc - margin, M * gridspc / 2])
#run the ode solver
fpts, t, l, P, Ptrace = mySolver(stokesFlowUpdater, y0, t0, dt, totalTime,
'adams', pdict)
#save the output
mat2py.write(fname + '_stokes.mat', {
't': t,
'fpts': fpts,
'pdict': pdictsave,
'dt': dt
})
#Viscoelastic run
print('VE flow...')
#use same initial conditions for spring as in Stokes flow, but add on Lagrangian points and stress
l0 = makeGrid(N, M, gridspc)
P0 = nm.zeros((N, M, 2, 2))
P0[:, :, 0, 0] = 1
P0[:, :, 1, 1] = 1
y0 = nm.append(nm.append(y0, l0.flatten()), P0.flatten())
#run the ode solver
fpts, t, l, P, Ptrace = mySolver(viscoElasticUpdater, y0, t0, dt,
totalTime, 'bdf', pdict)
#save the output
import numpy as nm
from scipy.integrate import ode
import mat2py
def f(t, y):
return nm.array([y[1], -y[0]])
if __name__ == '__main__':
y0, t0 = nm.array([0.25, 0.75]), 0
r = ode(f).set_integrator('dopri5')
r.set_initial_value(y0, t0)
t1 = 4 * nm.pi
dt = 4 * nm.pi / 1000
approx = nm.empty(0, )
while r.successful() and r.t < t1 + dt / 2.:
r.integrate(r.t + dt)
approx = nm.append(approx, r.y[0])
t = nm.arange(0, t1 + dt / 2., dt)
realsoln = 0.25 * nm.cos(t) + 0.75 * nm.sin(t)
mat2py.write('testsimpleode.mat', {
't': t,
'approx': approx,
'realsoln': realsoln
})
def mySprings():
#get ready to save files
import mat2py, os
#dictionary of variables for both Stokes flow and viscoelastic flow
pdictsave = dict(N=20,
M=20,
gridspc=1. / 20,
origin=[0, 0],
mu=1,
K=5,
xr=np.array([0.1]),
Wi=0.2)
pdictsave['beta'] = 1. / (2 * pdictsave['Wi'])
pdictsave['eps'] = 4 * pdictsave['gridspc']
pdict = pdictsave.copy()
pdict['myForces'] = calcForcesQuadraticSpring
pdict['blob'] = RS2D.CubicRegStokeslet(pdict['eps'], pdict['mu'])
pdict['blobderiv'] = RS2D.CubicRegStokesletDeriv(pdict['eps'], pdict['mu'])
gridspc = pdict['gridspc']
#set time parameters, save data every numskip time steps
t0 = 0
totalTime = 1
dt = 1.e-3
numskip = 100
#save file name
fname = os.path.expanduser('~/scratch/springtest')
#Stokes flow test, works
print('Stokes flow...')
#set up initial conditions
# margin = (N*gridspc-0.2)/2
# y0 = np.array([margin,M*gridspc/2,N*gridspc - margin,M*gridspc/2])
y0 = np.array([0.4, 0.5, 0.6, 0.5])
#run the ode solver
fpts, t, l, S, Strace = mySolver(stokesFlowUpdater, y0, t0, dt, totalTime,
'bdf', pdict, numskip)
#save the output
mat2py.write(fname + '_stokes_noC.mat', {
't': t,
'fpts': fpts,
'pdict': pdictsave,
'dt': dt
})
#Viscoelastic run
print('VE flow...')
#use same initial conditions for spring as in Stokes flow, but add on Lagrangian points and stress
N = pdict['N']
M = pdict['M']
l0 = makeGrid(N, M, gridspc, pdict['origin'])
P0 = np.zeros((N, M, 2, 2))
P0[:, :, 0, 0] = 1
P0[:, :, 1, 1] = 1
y0 = np.append(np.append(y0, l0.flatten()), P0.flatten())
#run the ode solver
fpts, t, l, S, Strace = mySolver(viscoElasticUpdaterKernelDeriv, y0, t0,
dt, totalTime, 'bdf', pdict, numskip)
#save the output
mat2py.write(
fname + '_visco_noC.mat', {
't': np.asarray(t),
'fpts': np.asarray(fpts),
'l': np.asarray(l),
'S': np.asarray(S),
'Strace': np.asarray(Strace),
'pdict': pdictsave,
'dt': dt
})
u_blob2 = vel2[0::2]
v_blob2 = vel2[1::2]
else:
u_blob1 = nm.append(u_blob1, vel1[0::2])
v_blob1 = nm.append(v_blob1, vel1[1::2])
u_blob2 = nm.append(u_blob2, vel2[0::2])
v_blob2 = nm.append(v_blob2, vel2[1::2])
fname = 'StokesCylTest_hattrapBEM_bothblobs' + (
4 - len(str(N))) * '0' + str(N) + '.mat'
mf.write(
fname, {
'u_blob1': u_blob1,
'v_blob1': v_blob1,
'u_blob2': u_blob2,
'v_blob2': v_blob2,
'exactu': exactu,
'exactv': exactv,
'obspts': obspts,
'blobparams': blobparams,
'numchords': numchords,
'M': M
})
print('Results in ' + fname)
#original method, both blobs, varying N
mu = 1.0
rad = 0.25
obspts = constructpatches()
exactu, exactv = exactSoln(obspts, rad, mu)
numchords = [2**k for k in range(3, 9)]
for N in numchords:
