examples.convection.exponential1DSource.tri2D

This example solves the steady-state convection-diffusion equation as described in examples.convection.exponential1D.mesh1D but uses a constant source value such that,

\[S_c = 1.\]

Here the axes are reversed (nx = 1, ny = 1000) and

\[\vec{u} = (0, 10)\]

>>> from fipy import CellVariable, Tri2D, DiffusionTerm, ExponentialConvectionTerm, DefaultAsymmetricSolver, Viewer
>>> from fipy.tools import numerix

>>> L = 10.
>>> nx = 1
>>> ny = 1000
>>> mesh = Tri2D(dx = L / ny, dy = L / ny, nx = nx, ny = ny)

>>> valueBottom = 0.
>>> valueTop = 1.

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

>>> var.constrain(valueBottom, mesh.facesBottom)
>>> var.constrain(valueTop, mesh.facesTop)

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

>>> eq = (-sourceCoeff - DiffusionTerm(coeff = diffCoeff)
...       - ExponentialConvectionTerm(coeff = convCoeff))

>>> eq.solve(var=var,
...          solver=DefaultAsymmetricSolver(tolerance=1.e-8, iterations=10000))

The analytical solution test for this problem is given by:

>>> axis = 1
>>> y = mesh.cellCenters[axis]
>>> AA = -sourceCoeff * y / convCoeff[axis]
>>> BB = 1. + sourceCoeff * L / convCoeff[axis]
>>> CC = 1. - numerix.exp(-convCoeff[axis] * y / diffCoeff)
>>> DD = 1. - numerix.exp(-convCoeff[axis] * L / diffCoeff)
>>> analyticalArray = AA + BB * CC / DD
>>> print(var.allclose(analyticalArray, atol = 1e-5))
1

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

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