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Calcolo
Published in: Calcolo 2/2024

01-06-2024

An asymptotic preserving scheme for the \(M_1\) model on polygonal and conical meshes

Authors: Xavier Blanc, Philippe Hoch, Clément Lasuen

Published in: Calcolo | Issue 2/2024

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Abstract

This work focuses on the design of a 2D numerical scheme for the \(M_1\) model on polygonal and conical meshes. This model is nonlinear and approximates the firsts moments of the radiative transfer equation using an entropic closure. Besides, this model admits a diffusion limit as the cross section goes to infinity. It is important for the numerical scheme to be consistent with this limit, that is to say, it should be asymptotic preserving or AP. Such a scheme already exists on polygonal meshes and the present work consists in adapting it to conical meshes. After introducing conical meshes, we explain the construction of the scheme. It is based on an analogy between the \(M_1\) model and the Euler gas dynamics system. We also present a second order reconstruction procedure and we apply it on both polygonal and conical meshes. In the last section, some numerical test cases are given so as to compare the nodal and conical schemes. The limit scheme is studied and we observe numerically that it is consistent with the diffusion equation.
previous article Numerical approximation of the stochastic Navier–Stokes equations through artificial compressibility
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Metadata
Title
An asymptotic preserving scheme for the model on polygonal and conical meshes
Authors
Xavier Blanc
Philippe Hoch
Clément Lasuen
Publication date
01-06-2024
Publisher
Springer International Publishing
Published in
Calcolo / Issue 2/2024
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-024-00574-4

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