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

Journal article

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

Authors: Fernández, EG; Díaz, MJC; Dumbser, M; de Luna, TM

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of Scientific Computing
• Volume: 90
• Issue: 1
• Pages: 52
• Article number: 52
• Publication date: 2021-12-17
• DOI: 10.1007/s10915-021-01734-2
• EISSN: 1573-7691
• ISSN: 0885-7474
• Language: Spanish
• Keywords: Discontinuous Galerkin method; Physics; Geometry; Applied mathematics; Finite element method; Mechanics; Flux limiter; Shallow water equations; Polygon mesh; Finite volume method; Discretization; Mathematical analysis; Computer science; Limiter; Classification of discontinuities; A priori and a posteriori; Mathematics