An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density

Abstract In this work, we present a novel numerical discretization of variable pressure multilayer shallow water model. The model can be written as hyperbolic PDE system and allows the simulation density driven gravity currents in framework. proposed consists an unlimited arbitrary high order accurate (ADER) Discontinuous Galerkin (DG) method, which is then limited with MOOD paradigm using posteriori subcell finite volume limiter. resulting scheme space time for smooth solutions does not destroy natural resolution inherent DG methods presence strong gradients or discontinuities. A strategy to preserve non-trivial stationary also discussed. final method very regions even coarse meshes, shown simulations presented here. Finally, comparison laboratory test, where empirical data are available, performed.