A Novel Fully Decoupled Scheme for the MHD System with Variable Density

In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) me...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 25; no. 1; pp. 215 - 236
Main Authors Wang, Zhaowei, Wang, Danxia, Jia, Hongen
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.01.2025
Walter de Gruyter GmbH
Subjects
65Mxx
65N12
65N22
65Nxx
Decoupling
Density
Error Analysis
Fully Decoupled
Gauge-Uzawa Method
Mathematical analysis
Mathematics
Unconditionally Stable
Variable Density
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ISSN1609-4840
1609-9389
DOI10.1515/cmam-2024-0004

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Summary:In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) method. And we prove its unconditional energy stability. Then we give the first-order finite element scheme and its implementation. Furthermore, we perform a rigorous error analysis of the proposed numerical scheme. Finally, we perform some numerical experiments to demonstrate the effectiveness of the decoupling scheme.
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2024-0004