WETTING AND DRYING TREATMENTS WITH MESH ADAPTATION FOR SHALLOW WATER EQUATIONS USING A RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD

Camille Poussel (1, 2) , Mehmet Ersoy (1, 2) , Frederic Golay (1, 2)

1 UTLN - Université de Toulon
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

This work is devoted to the numerical simulation of Shallow Water Equations involving dry areas, a moving shoreline and in the context of mesh adaptation. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Problems with dry areas are challenging for such methods. To counter this issue, special treatment is applied around the shoreline. This work compares three treatments, one based on Slope Modification, one based on p-adaptation and the last one based on eXtended Finite Element methods and mesh adaptation.

Mots clés: Discontinuous Galerkin; Shallow Water Equations; Wetting and drying; Positivity preserving; mesh adaptation SWE; Shallow Water Equations DG; Discontinuous Galerkin FE; Finite Element X-FE; eXtended Finite Element FV; Finite Volume AMR; Adaptive Mesh Refinement RK; Runge-Kutta SSP-RK; Strong Stability Preserving Runge-Kutta RKDG; Runge-Kutta Discontinuous Galerkin TVD; Total Variations Diminishing TVB; Total Variations Bounded CFD; Computational Fluid Dynamics CFL; Courant-Friedrichs-Lewy; DG; Discontinuous Galerkin; FE; Finite Element; X-FE; eXtended Finite Element; FV; Finite Volume; AMR; Adaptive Mesh Refinement; RK; Runge-Kutta; SSP-RK; Strong Stability Preserving Runge-Kutta; RKDG; Runge-Kutta Discontinuous Galerkin; TVD; Total Variations Diminishing; TVB; Total Variations Bounded; CFD; Computational Fluid Dynamics; CFL

Domaines: Mathématiques [math]

Camille Poussel, Mehmet Ersoy, Frederic Golay. WETTING AND DRYING TREATMENTS WITH MESH ADAPTATION FOR SHALLOW WATER EQUATIONS USING A RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD. 2024. ⟨hal-04676186⟩