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Dao, Tuan AnhNazarov, Murtazo
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A structure preserving numerical method for the ideal compressible MHD systemPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2024 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 508, article id 113009Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2024. Vol. 508, article id 113009
##### Keywords [en]

MHD, Vanishing viscosity limit, Structure preserving, Invariant domain, Involution constraints, Energy-stability
##### National Category

Computational Mathematics
##### Research subject

Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-532127DOI: 10.1016/j.jcp.2024.113009OAI: oai:DiVA.org:uu-532127DiVA, id: diva2:1872050
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##### Funder

Uppsala UniversitySwedish Research Council, 2021-04620Swedish Research Council, 2021-05095Available from: 2024-06-17 Created: 2024-06-17 Last updated: 2024-09-02
##### In thesis

We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations using a non-divergence formulation, where the contributions of the magnetic field to the momentum and total mechanical energy are treated as source terms. Our approach uses the Marchuk-Strang splitting technique and involves three distinct components: a compressible Euler solver, a source-system solver, and an update procedure for the total mechanical energy. The scheme allows for significant freedom on the choice of Euler's equation solver, while the magnetic field is discretized using a curl-conforming finite element space, yielding exact preservation of the involution constraints. We prove that the method preserves invariant domain properties, including positivity of density, positivity of internal energy, and the minimum principle of the specific entropy. If the scheme used to solve Euler's equation conserves total energy, then the resulting MHD scheme can be proven to preserve total energy. Similarly, if the scheme used to solve Euler's equation is entropy-stable, then the resulting MHD scheme is entropy stable as well. In our approach, the CFL condition does not depend on magnetosonic wave-speeds, but only on the usual maximum wavespeed from Euler's system. To validate the effectiveness of our method, we solve a variety of ideal MHD problems, showing that the method is capable of delivering second-order accuracy in space for smooth problems, while also offering unconditional robustness in the shock hydrodynamics regime as well.

1. Invariant domain preserving schemes for magnetohydrodynamics$(function(){PrimeFaces.cw("OverlayPanel","overlay1872071",{id:"formSmash:j_idt866:0:j_idt870",widgetVar:"overlay1872071",target:"formSmash:j_idt866:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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