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Stable finite difference schemes for the magnetic induction equation with Hall effect

Corti, Paolo ; Mishra, Siddhartha

In: BIT Numerical Mathematics, 2012, vol. 52, no. 4, p. 905-932

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    Titre
    • Stable finite difference schemes for the magnetic induction equation with Hall effect
    Auteur
    • Corti, Paolo. Seminar For Applied Mathematics (SAM), ETH Zentrum, Rämistrasse 101, 8092, Zürich, Switzerland
    • Mishra, Siddhartha. Seminar For Applied Mathematics (SAM), ETH Zentrum, Rämistrasse 101, 8092, Zürich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • BIT Numerical Mathematics, 2012, vol. 52, no. 4, p. 905-932. Springer Netherlands
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:318708
    Summary
    We consider a sub-model of the Hall-MHD equations: the so-called magnetic induction equations with Hall effect. These equations are non-linear and include third-order spatial and spatio-temporal mixed derivatives. We show that the energy of the solutions is bounded and design finite difference schemes that preserve the energy bounds for the continuous problem. We design both divergence preserving schemes and schemes with bounded divergence. We present a set of numerical experiments that demonstrate the robustness of the proposed schemes