Treffer: Entropy Stable Finite Difference Schemes for Chew, Goldberger and Low Anisotropic Plasma Flow Equations: Entropy stable finite difference schemes for Chew, Goldberger and Low anisotropic plasma flow equations

Title:
Entropy Stable Finite Difference Schemes for Chew, Goldberger and Low Anisotropic Plasma Flow Equations: Entropy stable finite difference schemes for Chew, Goldberger and Low anisotropic plasma flow equations
Authors:
Chetan Singh, Anshu Yadav, Deepak Bhoriya, Harish Kumar, Dinshaw S. Balsara
Source:
Journal of Scientific Computing. 102
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2025.
Publication Year:
2025
Subject Terms:
Method of lines for initial value and initial-boundary value problems involving PDEs, symmetrization, entropy stability, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, Shock waves and blast waves in fluid mechanics, Finite difference methods applied to problems in fluid mechanics, 65M06, 65M12, 65M20, 76P99 and 76W05, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Ionized gas flow in electromagnetic fields, plasmic flow, FOS: Mathematics, Magnetohydrodynamics and electrohydrodynamics, Mathematics - Numerical Analysis, higher-order finite difference schemes, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Weak solutions to PDEs, CGL equations
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1573-7691
0885-7474
DOI:
10.1007/s10915-024-02763-3
DOI:
10.48550/arxiv.2406.04783
Access URL:
http://arxiv.org/abs/2406.04783
https://zbmath.org/7975324
https://doi.org/10.1007/s10915-024-02763-3
Rights:
Springer Nature TDM
CC BY
Accession Number:
edsair.doi.dedup.....c21352a89bfb7775d3e01f1a8affe0cf
Database:
OpenAIRE

Weitere Informationen

In this article, we consider the Chew, Goldberger \& Low (CGL) plasma flow equations, which is a set of nonlinear, non-conservative hyperbolic PDEs modelling anisotropic plasma flows. These equations incorporate the double adiabatic approximation for the evolution of the pressure, making them very valuable for plasma physics, space physics and astrophysical applications. We first present the entropy analysis for the weak solutions. We then propose entropy-stable finite-difference schemes for the CGL equations. The key idea is to rewrite the CGL equations such that the non-conservative terms do not contribute to the entropy equations. The conservative part of the rewritten equations is very similar to the magnetohydrodynamics (MHD) equations. We then symmetrize the conservative part by following Godunov's symmetrization process for MHD. The resulting equations are then discretized by designing entropy conservative numerical flux and entropy diffusion operator based on the entropy scaled eigenvectors of the conservative part. We then prove the semi-discrete entropy stability of the schemes for CGL equations. The schemes are then tested using several test problems derived from the corresponding MHD test cases.