I am currently using a sweep loop to solve a differential equation (eq0) with respect to my cell variable phi using FiPy in python. Because my equation is non-linear, I am using a sweep loop as shown in an extract of my code below.
while res0 > resphi_tol:
res0 = eq0.sweep(var=phi, dt=dt)
But I keep getting the following error:
C:\Python27\lib\site-packages\fipy\variables\variable.py:1100: RuntimeWarning: invalid value encountered in power return self._BinaryOperatorVariable(lambda a,b: pow(a,b), other, value1mattersForUnit=True)
C:\Python27\lib\site-packages\fipy\variables\variable.py:1186: RuntimeWarning: invalid value encountered in less_equal return self._BinaryOperatorVariable(lambda a,b: a<=b, other)
Traceback (most recent call last):
.. File "SBM_sphere3.py", line 59, in
....res0 = eq0.sweep(var=phi, dt=dt)
.. File "C:\Python27\lib\site-packages\fipy\terms\term.py", line 207, in sweep
....solver._solve()
.. File "C:\Python27\lib\site-packages\fipy\solvers\pysparse\pysparseSolver.py", line 68, in _solve
....self.solve(self.matrix, array, self.RHSvector)
.. File "C:\Python27\lib\site-packages\fipy\solvers\pysparse\linearLUSolver.py", line 53, in _solve__
....LU = superlu.factorize(L.matrix.to_csr())
.. File "C:\Python27\lib\site-packages\pysparse\misc__init__.py", line 29, in newFunc
....return func(*args, **kwargs)
.. File "C:\Python27\lib\site-packages\pysparse__init__.py", line 47, in factorize
....return self.factorizeFnc(*args, **kwargs)
RuntimeError: Factor is exactly singular
I am pretty sure this error is due to term phi^(2/3) present in eq0. If I replace this term by abs(phi)^(2/3), the error goes away.
I assume the sweep loop returns a negative value for a few cells in phi at some point, resulting in error since we can't power a negative value with a non-integer exponent.
So my question is: is there a way to force sweep to avoid negative solutions?
I have tried to include a line that sets all negative values to 0 before sweeping:
while res0 > resphi_tol:
phi.setValue(0.,where=phi<0.)
res0 = eq0.sweep(var=phi, dt=dt)
The error is still there (because sweep tries to calculate the new matrix of coefficients just after solving the linearized system?).
Edit: I'm using Python 2.7.14 with FiPy 3.2. I'm sharing below the parts of my code which I think are relevant for the query. The entire code is quite extense. Some context: I'm solving balance equations for suspension flow. eq0 corresponds to the mass balance equation for the particle phase, and phi is the volume fraction of particles.
from pylab import *
from fipy import *
from fipy.tools import numerix
from scipy import misc
import osmotic_pressure_functions as opf
kic=96.91
lic=0.049
dt=1.e-2
steps=10
tol=1.e-6
Nx=8
Ny=4
Lx=Nx/Ny
dL=1./Ny
mesh = PeriodicGrid2DTopBottom(nx=Nx, ny=Ny, dx=dL, dy=dL)
x, y = mesh.cellCenters
phi = CellVariable(mesh=mesh, hasOld=True, value=0.,name='Volume fraction')
phi.constrain(0.01, mesh.facesLeft)
phi.constrain(0., mesh.facesRight)
rad=0.1
var1 = DistanceVariable(name='distance to center', mesh=mesh, value=numerix.sqrt((x-Nx*dL/2.)**2+(y-Ny*dL/2.)**2))
pi_ci = CellVariable(mesh=mesh, value=0.,name='Colloid-interface energy map')
pi_ci.setValue(kic*exp(-1.*(var1-rad)/(1.*lic)), where=(var1 > rad))
pi_ci.setValue(kic, where=(var1 <= rad))
def pi_cc_entr(x):
return opf.vantHoff(x)
def pi_cc_vdw(x):
return opf.van_der_waals(x,0.74,0.1)
def pi_cc(x):
return pi_cc_entr(x) + pi_cc_vdw(x)
diffusioncoeff = misc.derivative(pi_cc,phi,dx=1.e-6)
eq0 = TransientTerm() + ConvectionTerm(-pi_ci.faceGrad) == DiffusionTerm(coeff=diffusioncoeff)
step=0
t=0.
for step in range(steps):
print 'Step ', step
phi.updateOld()
res0 = 1e+10
while res0 > tol :
phi.setValue(0., where=phi<0)
res0 = eq0.sweep(var=phi, dt=dt) #ERROR HAPPENS HERE
Functions vantHoff and van_der_waals are being defined in a separate file.
def vantHoff(phi):
return phi
def van_der_waals(phi,phi_cp,nd_v):
return (nd_v*phi**3) / ((phi_cp-(phi_cp)**(1./3.)*(phi)**(2./3.))**2)
