Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation

On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical comple...

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Bibliographic Details
Published inarXiv.org
Main Authors Kaptsov, E I, Dorodnitsyn, V A, Meleshko, S V
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.05.2023
Subjects
Computer Science - Numerical Analysis
Conservation laws
Finite difference method
Magnetic flux
Magnetohydrodynamics
Mathematical analysis
Mathematics - Numerical Analysis
Physics - Fluid Dynamics
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Summary:On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky-Popov schemes. In the case of finite conductivity, schemes are derived that admit all the symmetries and possess all the conservation laws of the original differential model, including previously unknown conservation laws. In the case of a frozen-in magnetic field (when the conductivity is infinite), various schemes are constructed that possess conservation laws, including those preserving entropy along trajectories of motion. The peculiarities of constructing schemes with an extended set of conservation laws for specific forms of entropy and magnetic fluxes are discussed.
ISSN:2331-8422
DOI:10.48550/arxiv.2302.05280