FORCE schemes on unstructured meshes. I: Conservative hyperbolic systems. (English) Zbl 1168.65377

Summary: This paper is about the construction of numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple space dimensions on structured and unstructured meshes. The work is a multi-dimensional extension of the one-dimensional FORCE flux and is closely related to the work of Nessyahu-Tadmor and Arminjon [P. Arminjon and A. St-Cyr, Appl. Numer. Math. 46, No. 2, 135–155 (2003; Zbl 1025.65048); H. Nessyahu and E. Tadmore, J. Comput. Phys. 87, No. 2, 408–463 (1990; Zbl 0697.65068)]. The resulting basic flux is first-order accurate and monotone; it is then extended to arbitrary order of accuracy in space and time on unstructured meshes in the framework of finite volume and discontinuous Galerkin methods. The performance of the schemes is assessed on a suite of test problems for the multi-dimensional Euler and magneto-hydrodynamics equations on unstructured meshes.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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