Numerical oscillations Roe solver shallow water equations
I am using a finite volume shallow water model which uses the Roe Riemann solver. The scheme is only of 1st order and is applied to a structured rectangular grid, but I am still getting some nasty oscillations when simulating flows over a rather complex topography.
As far as I understand, this first order scheme should be stable (although highly diffusive); so my first guess for the cause of the oscillations is the treatment of the source terms (in this case bed topography).
Does anyone have a better guess/solution for this problem?
Your problem is most likely be related to the source term. When the discretization errors of the Roe solver and the source term are not compatible, errors and noise may grow in time without any physical forcing. Your solver will therefore not be able to maintain a 'quiet' water state over a complex topography. A possible solution to this problem are so-called 'well-balanced schemes' which can be found in numerous formulations in literature, e.g. by modifying the interface reconstruction or by upwinding the source term at the interfaces.
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