A numerical solution for moving boundary shallow water flow above parabolic bottom topography

Abstract

A numerical method has been applied to the nonlinear shallow water wave equations for unforced linear frictional flow above parabolic bottom topography and is found to be accurate. This solution involves moving shorelines. The motion decays over time. The numerical scheme used is adapted from the Selective Lumped Mass numerical scheme. The wetting and drying algorithm used in the numerical scheme is different to that in the Selective Lumped Mass scheme. The numerical scheme is finite element in space, using fixed triangular elements, finite difference in time and is explicit. The numerical solution compares well with an analytical solution. References

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