RT Journal Article
T1 An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density
A1 Guerrero Fernández, Ernesto
A1 Castro-Díaz, Manuel Jesús
A1 Dumbser, Michael
A1 Morales-de-Luna, Tomás
K1 Matemáticas aplicadas
AB 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 resolutioninherent 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 dataare available, is also performed.
PB Springer
YR 2021
FD 2021-12-17
LK https://hdl.handle.net/10630/24035
UL https://hdl.handle.net/10630/24035
LA eng
NO Fernández, E.G., Díaz, M.J.C., Dumbser, M. et al. An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density. J Sci Comput 90, 52 (2022). https://doi.org/10.1007/s10915-021-01734-2
NO Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 4 mar 2026