A MOOD-like compact high order Finite Volume scheme with Adaptive Mesh Refinement
Résumé
In this paper, a novel Finite Volume (FV) scheme for obtaining high order approximations of solutions of multidimensional hyperbolic systems of conservation laws within an Adaptive Mesh Refinement framework is proposed. It is based on a point-wise polynomial reconstruction that avoids the recalculation of reconstruction stencils and matrices whenever a mesh is refined or coarsened. It also couples both the limiting of the FV scheme and the refinement procedure, taking advantage of the Multi-dimensional Optimal Order Detection (MOOD) detection criteria. The resulting computational procedure is employed to simulate test cases of increasing difficulty using two models of Partial Differential Equations: the Euler system and the radiative M 1 model, thus demonstrating its efficiency.
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