THE NONLINEAR GALERKIN METHOD APPLIED TO SHALLOW WATER EQUATIONS

Bernard Di Martino (1, 2) , F. J. Chatelon , P. Orenga

1 SPE - Sciences pour l'environnement
2 Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]

In this work, we present some numerial approximations for a shallow water problem with a depth-mean velocity formulation and we give, where possible, an error bound. To prove the existence of solutions, we build a sequence of approximated solutions with the Galerkin method for the momentum equation and we solve the continuity equation with the method of the charateristics. This leads to an expensive natural numerical scheme. Then, in order to reduce the CPU time, we present other numerical approximations based on the linear or nonlinear Galerkin method.

Mots clés: Free surface flow; Galerkin method

Domaines: Mathématiques [math]

Bernard Di Martino, F. J. Chatelon, P. Orenga. THE NONLINEAR GALERKIN METHOD APPLIED TO SHALLOW WATER EQUATIONS. Mathematical Models and Methods in Applied Sciences, 1999, Mathematical Models and Methods in Applied Sciences, 09 (06), pp.825 - 854. ⟨10.1142/S0218202599000397⟩. ⟨hal-01630390⟩