A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows

The goal of this paper is to construct parallel solvers for 2d hyperbolic systems of conservation laws with source terms and nonconservative products. More precisely, finite volumes solvers on nonstructured grids are considered. The method of lines is applied: at every intercell a projected Riemann problem along the normal direction is considered which is discretized by means of the numerical schemes presented in [M.J. Castro, J. Macías, C. Parés. A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system, ESAIM: M2AN 35 (1) (2001) 107–127]. The resulting 2d numerical schemes are explicit and first order accurate. The solver is next parallelized by a domain decomposition technique. The specific application of the scheme to one- and two-layer shallow water systems has been implemented on a PC’s cluster. An efficient data structure based on OOMPI (C++ object oriented extension of MPI) has been developed to optimize the data exchange among the processors. Some numerical tests are next presented to validate the solver and the performance of its parallel implementation. Finally the two-layer shallow water model is applied to the simulation of the steady exchange through the Strait of Gibraltar.