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Titel
Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations / D. Kuzmin, N. Klyushnev
VerfasserKuzmin, D. ; Klyushnev, Nikita
ErschienenDortmund : Technische Universität Dortmund, Fakultät für Mathematik, June 2019
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (26 Seiten) : Illustrationen
SerieErgebnisberichte angewandte Mathematik ; no. 608
SchlagwörterFinite-Elemente-Methode / FCT-Verfahren / Magnetohydrodynamik
URNurn:nbn:de:hbz:6:2-126005 
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Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations [2.36 mb]
Zusammenfassung

This work introduces a new type of constrained algebraic stabilization for continuous piecewise-linear finite element approximations to the equations of ideal magnetohydrodynamics (MHD). At the first step of the proposed flux-corrected transport (FCT) algorithm, the Galerkin element matrices are modified by adding graph viscosity proportional to the fastest characteristic wave speed. At the second step, limited antidiffusive corrections are applied and divergence cleaning is performed for the magnetic field. The limiting procedure developed for this stage is designed to enforce local maximum principles, as well as positivity preservation for the density and thermodynamic pressure. Additionally, it adjusts the magnetic field in a way which penalizes divergence errors without violating conservation laws or positivity constraints. Numerical studies for 2D test problems are performed to demonstrate the ability of the proposed algorithms to accomplish this task in applications to ideal MHD benchmarks.

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