An Antidiffusive HLL Scheme for the Electronic $M_1$ Model in the Diffusion Limit

Chalons, Christophe; Guisset, Sébastien

doi:10.1137/18m1126692

Cited by 4 publications

(3 citation statements)

References 42 publications

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“…Let us assume in this paragraph that initial conditions are well-prepared. The scheme (21) and (22) can be rewritten as:…”

Section: Asymptotic Analysis Using the Convergence Speedsmentioning

confidence: 99%

“…Then the AP scheme (21) and (22) with (19) and p > 1/2, i + 1/2 = for all i, is L 2 stable and the following discrete entropy inequality holds:…”

Section: Theorem 31 Let Us Assume That the Following Cfl Condition Hmentioning

confidence: 99%

“…Furthermore, this second semi-implicit scheme can be understood as a Godunov-type scheme associated with an Approximate Riemann Solver. In order to show this, we follow the same approach as the one recently given in [21] and extending the ideas of [1,22].…”

Section: Another Semi-implicit Scheme and Its Equivalent Formulation mentioning

confidence: 99%

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High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations

Chalons

Turpault

2019

Numerical Methods Partial

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Funding informationAgence Nationale de la Recherche, ANR-14-CE25-0001-03.In this work, we address the numerical approximation of linear systems with possibly stiff source terms which induce an asymptotic diffusion limit. More precisely, we are interested in the design of high-order asymptotic-preserving schemes. Our approach is based on a very simple modification of the numerical flux associated with the usual HLL scheme. This alteration can be understood as a numerical diffusion reduction technique and allows to capture the correct asymptotic behavior in the diffusion limit and to consider uniformly high-order extensions. We more specifically consider the case of the Goldstein-Taylor model but the overall approach is shown to be easily adapted to more general systems. KEYWORDSasymptotic-preserving schemes, diffusion limit for linear hyperbolic systems, high order finite volumes schemes 1

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“…Let us assume in this paragraph that initial conditions are well-prepared. The scheme (21) and (22) can be rewritten as:…”

Section: Asymptotic Analysis Using the Convergence Speedsmentioning

confidence: 99%

“…Then the AP scheme (21) and (22) with (19) and p > 1/2, i + 1/2 = for all i, is L 2 stable and the following discrete entropy inequality holds:…”

Section: Theorem 31 Let Us Assume That the Following Cfl Condition Hmentioning

confidence: 99%

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High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations

Chalons

Turpault

2019

Numerical Methods Partial

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Asymptotic preserving schemes on conical unstructured 2D meshes

Blanc

Delmas

Hoch

2021

Numerical Methods in Fluids

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In this article, we consider the hyperbolic heat equation. This system is linear hyperbolic with stiff source terms and satisfies a diffusion limit. Some finite volume numerical schemes have been proposed which reproduce this diffusion limit. Here, we extend such schemes, originally defined on polygonal meshes, to conical meshes (using rational quadratic Bezier curves). We obtain really new schemes that do not reduce to the polygonal version when the conical edges tend to straight lines. Moreover, these schemes can handle curved unstructured meshes so that geometric error on initial data representation is reduced and geometry of the domain is improved. Extra flux coming from conical edge (through his midedge point) has a deep impact on the stabilization when compared with the original polygonal scheme. Cross-stencil phenomenon of polygonal scheme has disappeared, and issue of positivity for the diffusion problem (although unresolved on distorted mesh and/or with varying cross-section) has been in some sense improved.

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An asymptotic preserving scheme for the $$M_1$$ model on polygonal and conical meshes

Blanc,

Hoch,

Lasuen

2024

Calcolo

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An Antidiffusive HLL Scheme for the Electronic $M_1$ Model in the Diffusion Limit

Cited by 4 publications

References 42 publications

High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations

High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations

Asymptotic preserving schemes on conical unstructured 2D meshes

An asymptotic preserving scheme for the $$M_1$$ model on polygonal and conical meshes

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