Title :

Positivity-preserving schemes for Euler equations: Sharp and practical CFL conditions

Author(s) :

Calgaro, Caterina [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Creusé, Emmanuel [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Goudon, Thierry [Auteur]
COmplex Flows For Energy and Environment [COFFEE]
Penel, Yohan [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Numerical Analysis, Geophysics and Ecology [ANGE]

Journal title :

Journal of Computational Physics

Pages :

417--438

Publisher :

Elsevier

Publication date :

2013

ISSN :

0021-9991

English keyword(s) :

Positivity-preserving MUSCL schemes
2nd-order finite volume method
Euler equations
CFL condition
τ-limiters.
τ-limiters

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

When one solves PDEs modelling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same ...
Show more >When one solves PDEs modelling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. For instance, the underlying physical assumptions for the Euler equations are the positivity of both den- sity and pressure variables. We consider in this paper an unstructured vertex-based tesselation in R2 . Given a MUSCL finite volume scheme and given a reconstruction method (including a limiting process), the point is to determine whether the overall scheme ensures the positivity. The present work is issued from seminal papers from Perthame and Shu (On positivity preserving finite volume schemes for Euler equations, Numer. Math. 73 (1996) 119-130) and Berthon (Robustness of MUSCL schemes for 2D unstructured meshes, J. Comput. Phys. 218 (2) (2006) 495-509). They proved in different frameworks that under assumptions on the cor- responding one-dimensional numerical flux, a suitable CFL condition guarantees that den- sity and pressure remain positive. We first analyse Berthon's method by presenting the ins and outs. We then propose a more general approach adding non geometric degrees of freedom. This approach includes an optimization procedure in order to make the CFL condition explicit and as less restric- tive as possible. The reconstruction method is handled independently by means of s- limiters and of an additional damping parameter. An algorithm is provided in order to specify the adjustments to make in a preexisting code based on a certain numerical flux. Numerical simulations are carried out to prove the accuracy of the method and its ability to deal with low densities and pressures.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL