On the best quantity reconstructions for a well balanced finite volume method used to solve the shallow water wave equations with a wet/dry interface

Well balanced finite volume methods used to solve the shallow water wave equations are designed to preserve the steady state of a 'lake at rest'. Unfortunately, for problems involving wet/dry interfaces, this steady state is not preserved unless the involved quantities are reconstructed with care. We test four reconstruction options: stage and momentum (where bed is fixed); stage and velocity (where bed is fixed); stage, water height, and velocity; and stage, bed, and velocity (with modification at wet/dry interfaces). Reconstructions based on stage, water height, and velocity are shown to preserve the steady state problem and accurately solve a representative unsteady state problem, whereas the other options lead to problems in both maintaining the steady solution and accurately solving non-steady problems. Our results indicate the appropriate choice of reconstruction variables for various situations when solving the shallow water wave equations using finite volume methods.