Geodesic
Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)
ESAIM: Mathematical Modelling and Numerical Analysis , Multiscale problems and techniques. Special Issue, Tome 48 (2014) no. 2, pp. 583-602

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/m2an/2013105
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 },
     pages = {583--602},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {2},
     year = {2014},
     doi = {10.1051/m2an/2013105},
     mrnumber = {3177858},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013105/}
}
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 
PY  - 2014
SP  - 583
EP  - 602
VL  - 48
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013105/
DO  - 10.1051/m2an/2013105
LA  - en
ID  - M2AN_2014__48_2_583_0
ER  - 
%0 Journal Article
%A Berthon, Christophe
%A Coudière, Yves
%A Desveaux, Vivien
%T Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2014
%P 583-602
%V 48
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013105/
%R 10.1051/m2an/2013105
%G en
%F 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 , Multiscale problems and techniques. Special Issue, Tome 48 (2014) no. 2, pp. 583-602. doi: 10.1051/m2an/2013105

Cité par Sources :