An asymptotic preserving scheme with the maximum principle for the \(M_1\) model on distorded meshes

DOI10.1016/j.crma.2012.07.002zbMath1257.65053OpenAlexW2046069759MaRDI QIDQ447896

Christophe Buet, Emmanuel Franck, Bruno Després

Publication date: 30 August 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2012.07.002

zbMATH Keywords

maximum principlefinite volume methodnumerical examplessemidiscretizationlinear transport equationdistorded meshesEulerian schemegas dynamic model

Mathematics Subject Classification ID

Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) First-order hyperbolic equations (35L02)

Related Items (6)

Finite volume scheme with local high order discretization of the hydrostatic equilibrium for the Euler equations with external forces ⋮ Modified Finite Volume Nodal Scheme for Euler Equations with Gravity and Friction ⋮ Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes ⋮ Asymptotic preserving schemes on distorted meshes for Friedrichs systems with stiff relaxation: application to angular models in linear transport ⋮ An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction ⋮ Stabilized mixed finite element method for the \(M_1\) radiation model

Cites Work

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• A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension
• An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations
• Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
• An HLLC scheme to solve the \(M_{1}\) model of radiative transfer in two space dimensions
• Asymptotic Preserving Finite Volumes Discretization For Non-Linear Moment Model On Unstructured Meshes
• A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems
• The Convergence Rate of Approximate Solutions for Nonlinear Scalar Conservation Laws
• A Free Streaming Contact Preserving Scheme for the M₁ Model

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