# Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)

Christophe Berthon; Yves Coudière; Vivien Desveaux

- Volume: 48, Issue: 2, page 583-602
- ISSN: 0764-583X

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topBerthon, Christophe, Coudière, Yves, and Desveaux, Vivien. "Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.2 (2014): 583-602. <http://eudml.org/doc/273187>.

@article{Berthon2014,

abstract = {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.},

author = {Berthon, Christophe, Coudière, Yves, Desveaux, Vivien},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {systems of conservation laws; muscl method; unstructured meshes; dual mesh; invariant region; monotone upwind schemes for conservation laws (MUSCL); Courant-Friedrichs-Lewy (CFL) conditions; gradient reconstruction; numerical experiment},

language = {eng},

number = {2},

pages = {583-602},

publisher = {EDP-Sciences},

title = {Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)},

url = {http://eudml.org/doc/273187},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Berthon, Christophe

AU - Coudière, Yves

AU - Desveaux, Vivien

TI - Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 2

SP - 583

EP - 602

AB - 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.

LA - eng

KW - systems of conservation laws; muscl method; unstructured meshes; dual mesh; invariant region; monotone upwind schemes for conservation laws (MUSCL); Courant-Friedrichs-Lewy (CFL) conditions; gradient reconstruction; numerical experiment

UR - http://eudml.org/doc/273187

ER -

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