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Better choice of CFL number definition

Open bangerth opened this issue 3 years ago • 0 comments

We currently compute the time step based on a CFL number that defines h as the shortest edge length of a cell: https://github.com/geodynamics/aspect/blob/main/source/time_stepping/convection_time_step.cc#L48-L75

That seemed natural to FEM people like Timo and me at the time, but it's not actually what the hyperbolic equations community commonly uses. Rather, they use a definition of h that is the diameter of the cell in the direction of flow. This is always at least the size of the shortest edge, but may be substantially larger -- up to sqrt(3) times the shortest edge for cubes, for example.

I think it would be interesting to implement this in ASPECT in place of the current definition. It would mean having to take larger time steps, but we would have to assess whether that impacts the accuracy of the solutions we get.

bangerth avatar Feb 11 '22 22:02 bangerth