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

Author

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  • Loubère, Raphaël
  • Turpault, Rodolphe
  • Bourriaud, Alexandre

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.

Suggested Citation

  • Loubère, Raphaël & Turpault, Rodolphe & Bourriaud, Alexandre, 2023. "A MOOD-like compact high order finite volume scheme with adaptive mesh refinement," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008608
    DOI: 10.1016/j.amc.2022.127792
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    References listed on IDEAS

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    1. Buchmüller, Pawel & Dreher, Jürgen & Helzel, Christiane, 2016. "Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 460-478.
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