examples.convection.exponential2D.mesh2D

This example solves the steady-state convection-diffusion equation as described in examples.convection.exponential1D.mesh1D on a 2D mesh with nx = 10 and ny = 10:

>>> from fipy import CellVariable, Grid2D, DiffusionTerm, ExponentialConvectionTerm, DefaultAsymmetricSolver, Viewer
>>> from fipy.tools import numerix

>>> L = 10.
>>> nx = 10
>>> ny = 10
>>> mesh = Grid2D(L / nx, L / ny, nx, ny)

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

>>> var = CellVariable(name = "concentration",
...                    mesh = mesh,
...                    value = valueLeft)

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

>>> diffCoeff = 1.
>>> convCoeff = (10., 0.)

>>> eq = DiffusionTerm(coeff=diffCoeff) + ExponentialConvectionTerm(coeff=convCoeff)

>>> eq.solve(var = var,
...          solver=DefaultAsymmetricSolver(tolerance=1.e-15, iterations=10000))

We test the solution against the analytical result:

>>> axis = 0
>>> x = mesh.cellCenters[axis]
>>> CC = 1. - numerix.exp(-convCoeff[axis] * x / diffCoeff)
>>> DD = 1. - numerix.exp(-convCoeff[axis] * L / diffCoeff)
>>> analyticalArray = CC / DD
>>> print(var.allclose(analyticalArray, rtol = 1e-10, atol = 1e-10))
1

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

Last updated on Feb 07, 2025. Created using Sphinx 7.1.2.