An arbitrary high order ADER Discontinous Galerking (DG) numerical scheme for the multilayer shallow water model with variable density

Abstract

In this work, an arbitrary high order numerical discretization for a density dependent multilayer shallow-water model is presented. The model can be written as a system of hyperbolic PDE equations and it is especially suited for simulations of density driven gravity currents within the shallow-water framework. The proposed discretization is composed by an unlimited high order accurate (ADER) Discontinuous Galerkin (DG) method, which is then limited a posteriori with the MOOD paradigm, resulting in great resolution capabilities in smooth regions alongside a robust and accurate respond for strong gradients or discontinuities. A numerical strategy to preserve non-trivial stationary solutions is also discussed. Some numerical results are shown including density driven currents where laboratory data is available.