We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation procedure to enforce the required robustness property. Indeed, the invariant region is usually preserved at the expense of a more restrictive CFL condition. Here, we try to optimize this condition in order to reduce the computational cost.

Classification: 65M12, 35L65, 76M12

Keywords: systems of conservation laws, muscl method, unstructured meshes, dual mesh, invariant region

@article{M2AN_2014__48_2_583_0, author = {Berthon, Christophe and Coudi\`ere, Yves and Desveaux, Vivien}, title = {Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {48}, number = {2}, year = {2014}, pages = {583-602}, doi = {10.1051/m2an/2013105}, mrnumber = {3177858}, language = {en}, url = {http://www.numdam.org/item/M2AN_2014__48_2_583_0} }

Berthon, Christophe; Coudière, Yves; Desveaux, Vivien. Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR). ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 2, pp. 583-602. doi : 10.1051/m2an/2013105. http://www.numdam.org/item/M2AN_2014__48_2_583_0/

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