A MOOD-like compact high order finite volume scheme with adaptive mesh refinement

Raphaël Loubère, Rodolphe Turpault and Alexandre Bourriaud

Applied Mathematics and Computation, 2023, vol. 443, issue C

Abstract: In this paper, a novel Finite Volume (FV) scheme for obtaining high order approximations of solutions of multi-dimensional 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 M1 model, thus demonstrating its efficiency.

Keywords: Finite Volume scheme; High accuracy; Hyperbolic systems; MOOD; AMR (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008608

DOI: 10.1016/j.amc.2022.127792

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