examples.diffusion.steadyState.mesh1D.inputPeriodic

One can then solve the same problem as in examples/diffusion/steadyState/mesh1D/input.py but with a periodic mesh and no boundary conditions. The periodic mesh is used to simulate periodic boundary conditions.

>>> from fipy import PeriodicGrid1D, CellVariable, TransientTerm, DiffusionTerm, Viewer

>>> nx = 50
>>> dx = 1.
>>> mesh = PeriodicGrid1D(nx = nx, dx = dx)

The variable is initially a line varying form valueLeft to valueRight.

>>> valueLeft = 0
>>> valueRight = 1
>>> x = mesh.cellCenters[0]

>>> Lx = nx * dx
>>> initialArray = valueLeft + (valueRight - valueLeft) * x / Lx
>>> var = CellVariable(name = "solution variable", mesh = mesh,
...                                                value = initialArray)

>>> from fipy import input
>>> if __name__ == '__main__':
...     viewer = Viewer(vars=var, datamin=0., datamax=1.)
...     viewer.plot()
...     input("press key to continue")

A TransientTerm is used to provide some fixed point, otherwise the solver has no fixed value and can become unstable.

>>> eq = TransientTerm(coeff=1e-8) - DiffusionTerm()

The initial residual is much larger than the norm of the right-hand-side vector, so we use “initial” tolerance scaling with a tolerance that will drive to an accurate solution.

>>> solver = eq.getDefaultSolver(criterion="initial", tolerance=1e-8)
>>> eq.solve(var=var, dt=1., solver=solver)

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

The result of the calculation will be the average value over the domain.

>>> print(var.allclose((valueLeft + valueRight) / 2., rtol = 1e-5))
True

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