An asymptotic preserving scheme for hydrodynamics radiative transfer models

Buet, Christophe; Cordier, Stéphane

doi:10.1007/s00211-007-0094-x

Cited by 50 publications

(67 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the next section, three of them are given namely the Telegraph model [10,11], the Euler equations with high friction [1,12] and the M1 model for radiative transfer [2,11,[13][14][15]. All of them involve their own numerical schemes (see [1,2,10] for a brief overview of the numerical procedures, see also [5,[16][17][18][19][20][21][22] for some related works).…”

Section: Introductionmentioning

confidence: 98%

Asymptotic preserving HLL schemes

Berthon

Turpault

2010

Numer. Methods Partial Differential Eq.

110

View full text Add to dashboard Cite

This work concerns the derivation of HLL schemes to approximate the solutions of systems of conservation laws supplemented by source terms. Such a system contains many models such as the Euler equations with high friction or the M1 model for radiative transfer. The main difficulty arising from these models comes from a particular asymptotic behavior. Indeed, in the limit of some suitable parameter, the system tends to a diffusion equation. This article is devoted to derive HLL methods able to approximate the associated transport regime but also to restore the suitable asymptotic diffusive regime. To access such an issue, a free parameter is introduced into the source term. This free parameter will be a useful correction to satisfy the expected diffusion equation at the discrete level. The derivation of the HLL scheme for hyperbolic systems with source terms comes from a modification of the HLL scheme for the associated homogeneous hyperbolic system. The resulting numerical procedure is robust as the source term discretization preserves the physical admissible states. The scheme is applied to several models of physical interest. The numerical asymptotic behavior is analyzed and an asymptotic preserving property is systematically exhibited. The scheme is illustrated with numerical experiments.

show abstract

Section: Introductionmentioning

confidence: 98%

Asymptotic preserving HLL schemes

Berthon

Turpault

2010

Numer. Methods Partial Differential Eq.

110

View full text Add to dashboard Cite

show abstract

“…In addition, it can be easily proved that (8) with λ = 0 is strictly hyperbolic with three eigenvalues given by −a, 0 and a which are nothing but approximations of the exact eigenvalues −ρc, 0 and ρc for system (7). Then and in particular, the subcharacteristic condition means that information propagates faster in the relaxation model.…”

Section: Relaxation Approximation Of the Homogeneous Modelmentioning

confidence: 99%

“…We propose in this section a relaxation approximation of the Lagragian system (7). The main objective is to overcome the non linearities that make difficult the resolution of this system.…”

Section: Relaxation Approximationmentioning

confidence: 99%

“…Such property is referred to as an asymptotic preserving (AP) property. Since its introduction in the pioneer work of [23,25], the notion of AP numerical schemes has been investigated and implemented in the past years in a wide range of context stemming from hydrodynamics with radiative transfer [22,8,7,2,4], multiscale kinetics [24], diffusive limit of the transport equation [26,29] to problems similar to our model [6,4,11]. Without being exhaustive, we also refer the reader to [9,16,3,1,26].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms

Chalons¹,

Girardin²,

Kokh³

2013

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

We propose a large time step and asymptotic preserving scheme for the gas dynamics equations with external forces and friction terms. By asymptotic preserving, we mean that the numerical scheme is able to reproduce at the discrete level the parabolic-type asymptotic behaviour satisfied by the continuous equations. By large time-step, we mean that the scheme is stable under a CFL stability condition driven by the (slow) material waves, and not by the (fast) acoustic waves as it is customary in Godunov-type schemes. Numerical evidences are proposed and show a gain of several orders of magnitude in both accuracy and efficiency.

show abstract

“…During the last decade, several asymptotic-preserving schemes were proposed in the literature and we refer for instance to [10,17,13,14,9,7,6,11] for some of the most recent ones, but also to the references proposed therein. These schemes are able to give a suitable numerical approximation in the limit of both ε large and small.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms

Berthon

Chalons

Turpault

2012

Numerical Methods Partial

View full text Add to dashboard Cite

To cite this version:Christophe Berthon, Christophe Chalons, Rodolphe Turpault. Asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation terms. Numerical Methods for Partial Differential Equations, Wiley, 2012, vol 29 (4) AbstractWe devise a new-class of asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation source terms governed by a relaxation time ε. As an alternative to classical operator-splitting techniques, the objectives of these schemes are twofold: first, to give accurate numerical solutions for large, small and in-between values of ε and second, to make optional the choice of the numerical scheme in the asymptotic regime ε tends to zero. The latter property may be of particular interest to make easier and more efficient the coupling at a fixed spatial interface of two models involving very different values of ε.

show abstract

An asymptotic preserving scheme for hydrodynamics radiative transfer models

Cited by 50 publications

References 18 publications

Asymptotic preserving HLL schemes

Asymptotic preserving HLL schemes

Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms

Asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms

Contact Info

Product

Resources

About