Genuinely multidimensional evolution Galerkin schemes for the shallow water equations

Summary

The main objective of this contribution is to present a new genuinely multidimensional finite volume scheme for the shallow water equations. Our approach couples a finite volume formulation with an approximate evolution operator. The latter is constructed using bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. In order to achieve monotone and genuinely multidimensional FV scheme it is suitable to use Simpson’s rule approximation of the flux integrals along the cell interfaces. The experimental tests confirm good multidimensional properties of the scheme, e.g., preservation of rotational symmetry and monotonicity.