A generalized finite difference method for the 2-D nonlinear shallow water equations

Mansour Dia Ben (1, 2) , Ababacar Diagne (3, 1) , Leon Matar Tine (4, 5, 1, 6)

1 LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
2 Comput., Electr., & Math. Sci. of Eng. (CEMSE) Div.
3 Division of Scientific Computing
4 ICJ - Institut Camille Jordan
5 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
6 MMCS - Modélisation mathématique, calcul scientifique

In this paper, we propose a generalized finite difference method for two-dimensional non-linear shallow equations. The space discretization uses the staggered grid C of Arakawa. Beside the implicit-explicit factor theta, the time discretization involves a balance ratio alpha of the spatial nodes. The stability analysis takes account the size of the parameters. We discuss the stabilizing properties of the scheme and present some numerical experiments.

Mots clés: Finite difference methods; Shallow water equations; Stability analysis

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Mansour Dia Ben, Ababacar Diagne, Leon Matar Tine. A generalized finite difference method for the 2-D nonlinear shallow water equations. CARI'14 Colloque Africain sur la Recherche en Informatique et en Mathématiques Appliquées., Oct 2014, Saint-Louis, Senegal. ⟨hal-01104586⟩