Revisiting energy estimates of the CPR scheme for the Shallow Water equations
Résumé
The present notes concern some improvements concerning the CPR (Centred Potential Regularization) schemes proposed in [M. Parisot, J.P. Vila, 2016] and [F. Couderc et al., 2017] in the particular case of the Shallow Water equations. We propose here a totally explicit variant of the scheme introduced in [F. Couderc et al., 2017], and clarify the time step condition required to get energy dissipation (in other terms, entropy stability). This work aslo results in a slight modification of the viscosity terms, that may help improving numerical results far from low-Froude regimes. This document is organized as follows: in Section 1 we introduce the main notations as well as elementary technical lemmas concerning the discrete operators. The numerical scheme is given in Section 2, together with preliminary results regarding the discrete energy. The main stability results are discussed in Section 3, and extended in 2D in Section 4.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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