examples.convection.peclet

This example tests diffusion-convection for increasing Péclet numbers. This test case has been introduced because LinearCGSSolver was not working with Péclet numbers over 1. LinearLUSolver is now the default for ConvectionTerm. For nx = 1000 the LinearGMRESSolver does not work.

>>> from fipy import CellVariable, Grid1D, TransientTerm, DiffusionTerm, PowerLawConvectionTerm, Viewer
>>> from fipy.tools import numerix

>>> L = 1.
>>> nx = 1000
>>> dx =  L / nx
>>> mesh = Grid1D(dx=dx, nx=nx)

>>> valueLeft = 0.
>>> valueRight = 1.

>>> var = CellVariable(name = "solution variable", mesh=mesh, value=valueLeft)

>>> var.constrain(valueLeft, mesh.facesLeft)
>>> var.constrain(valueRight, mesh.facesRight)

>>> if __name__ == '__main__':
...     viewer = Viewer(vars = var)

>>> convCoeff = 1.0
>>> peclet = 1e-3
>>> allcloseList = []
>>> from fipy import input
>>> from builtins import str
>>> while peclet < 1e4:
...     var[:] = valueLeft
...     diffCoeff = convCoeff * dx / peclet
...     eq = (TransientTerm(1e-4)
...           == DiffusionTerm(coeff=diffCoeff)
...           + PowerLawConvectionTerm(coeff=(convCoeff,)))
...     eq.solve(var=var, dt=1.)
...     x = mesh.cellCenters[0]
...     arg0 = -convCoeff * x / diffCoeff
...     arg0 = numerix.where(arg0 < -200, -200, arg0)
...     arg1 = -convCoeff * L / diffCoeff
...     arg1 = (arg1 >= -200) * (arg1 + 200) - 200
...     CC = 1. - numerix.exp(arg0)
...     DD = 1. - numerix.exp(arg1)
...     analyticalArray = CC / DD
...     allcloseList.append(var.allclose(CC / DD, rtol = 1e-2, atol = 1e-2).value)
...     if __name__ == '__main__':
...         viewer.plot()
...         input("Peclet number: " + str(peclet) + ", press key")
...     peclet *= 10

>>> print(allcloseList)
[True, True, True, True, True, True, True]

Last updated on Feb 06, 2025. Created using Sphinx 7.1.2.