Unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections

SUMMARY In this article, we propose different splitting procedures for the transient incompressible magnetohydrodynamics (MHD) system that are unconditionally stable. We consider two levels of splitting, on one side we perform the segregation of the fluid pressure and magnetic pseudo‐pressure from t...

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Vydáno v:International journal for numerical methods in engineering Ročník 93; číslo 3; s. 302 - 328
Hlavní autoři: Badia, Santiago, Planas, Ramon, Gutiérrez-Santacreu, Juan Vicente
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Chichester, UK John Wiley & Sons, Ltd 20.01.2013
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John Wiley & Sons
Témata:
Anàlisi numèrica
Computational fluid dynamics
Finite element method
Fluid flow
fractional step methods
Física
Física de fluids
incompressible magnetohydrodynamics
Magnetohidrodinàmica
Magnetohydrodynamics
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Models matemàtics
Mètodes en elements finits
operator splitting algorithms
Segregations
Splitting
stabilized finite element methods
symmetric projection stabilization
Àrees temàtiques de la UPC
ISSN:0029-5981, 1097-0207
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Shrnutí:SUMMARY In this article, we propose different splitting procedures for the transient incompressible magnetohydrodynamics (MHD) system that are unconditionally stable. We consider two levels of splitting, on one side we perform the segregation of the fluid pressure and magnetic pseudo‐pressure from the vectorial fields computation. At the second level, the fluid velocity and induction fields are also decoupled. This way, we transform a fully coupled indefinite multi‐physics system into a set of smaller definite ones, clearly reducing the CPU cost. With regard to the finite element approximation, we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization, allows to circumvent inf‐sup conditions (clearly simplifying implementation issues), and is able to capture non‐smooth solutions of the magnetic subproblem. However, residual‐based finite element formulations are not suitable for segregation, because they lose the skew‐symmetry of the off‐diagonal blocks. Therefore, in this work, we have proposed a novel term‐by‐term stabilization of the MHD system based on projections that is still unconditionally convergent. Copyright © 2012 John Wiley & Sons, Ltd.
Bibliografie:ArticleID:NME4392
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4392