WETTING AND DRYING TREATMENTS WITH MESH ADAPTATION FOR SHALLOW WATER EQUATIONS USING A RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD
Résumé
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]| Origine | Fichiers produits par l'(les) auteur(s) |
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