Phase behavior of a finite volume shallow water algorithm

Two algorithms that have been used for shallow water simulations on unstructured meshes are the generalized wave continuity (GWC) algorithm and selective mass lumping (SLFE). Both produce noise free solutions; the former by its ability to propagate short wave components, and the latter by its ability to damp the short waves that are not propagated. Recently, the finite volume method, which has been used in gas dynamics, has emerged as the basis for another solution algorithm on unstructured meshes. Advantages include its ability to conserve mass at an element level and its ability to handle shocks in the solution (supercritical flow problems). Herein we demonstrate that the phase propagation behavior, as represented by Fourier analysis, of the low-order finite volume method is more similar to SLFE than GWC. On the other hand, with the proper choice of parameters, the dispersion relation for the finite volume method is more similar to the GWC than SLFE. Thus, the algorithm can uniquely resolve all frequencies with minimal damping.