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Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System

In: Analysis and Numerics for Conservation Laws

Author

Listed:
  • A. Dedner

    (Mathematisches Institut der Albert-Ludwigs Universität Freiburg)

  • D. Kröner

    (Mathematisches Institut der Albert-Ludwigs Universität Freiburg)

  • C. Rohde

    (Mathematisches Institut der Albert-Ludwigs Universität Freiburg)

  • M. Wesenberg

    (Behr GmbH & Co. KG, Technologiecenter, Methodenentwicklung 3D Simulation)

Abstract

Summary The equations of compressible radiation magnetohydrodynamics provide a widely accepted mathematical model for the basic fluid-dynamical processes in the sun's atmosphere. From the mathematical point of view the equations constitute an instance of a system of non-local hyperbolic balance laws. We have developed and implemented numerical methods in three space dimensions on the basis of a finite volume scheme that allow the efficient approximation of weak solutions. Key features are the use of efficient Riemann solvers, a special treatment of the divergence constraint, higher-order schemes, the extended short characteristics method, local mesh adaption, and parallelization using dynamic load balancing. Moreover, methods to cope with the special nature of the atmosphere are included. In this contribution we give an overview of our work, highlight our most important results, and report on some new developments. In particular, we present a scalar model problem for which an almost complete analytical treatment is possible.

Suggested Citation

  • A. Dedner & D. Kröner & C. Rohde & M. Wesenberg, 2005. "Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System," Springer Books, in: Gerald Warnecke (ed.), Analysis and Numerics for Conservation Laws, pages 163-202, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27907-5_8
    DOI: 10.1007/3-540-27907-5_8
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