A three-dimensional FVC scheme on non-uniform tetrahedron meshes: application to the 3D Euler equation

Summary

This study is about the construction of a numerical scheme of the predictor-corrector type in conservative form for solving general systems of conservation laws in multiple space dimensions on unstructured meshes. The work is a generalization of the one-dimensional finite volume characteristics (FVC) scheme and is related to the work of Fayssal Benkhaldoun and Mohammed Sead. The construction of the intermediate state is based on the method of characteristics, while the corrective stage recovers the conservation equations. The scheme is accurate to first order, monotonic and entropic; it avoids Riemann solvers at each interface; it also allows for improved accuracy order in time and space on unstructured three-dimensional meshes in the framework of the finite volume method. The scheme's performance is evaluated through a series of test benchmarks for the three-dimensional version of the Euler equations..

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