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Absorbing Boundary Conditions for Astrophysical MHD Simulations

  • A. Dedner
  • D. Kröner
  • M. Wesenberg
  • I. Sofronov

Abstract

Many problems for systems of conservation laws are formulated either on infinite domains or on domains which are by orders of magnitude larger than the interesting structures. In the first case, it is often impossible to find an exact representation of the problem which is suitable for numerical simulations. But even in the second case it can be difficult to perform the simulation on the whole domain, since much computational effort is wasted in uninteresting regions. Therefore the size of the computational domain has to be reduced, which introduces new boundaries without physical meaning. At these artificial boundaries suitable boundary conditions for the PDEs have to be formulated.

In this paper we will discuss a method to derive artificial non-reflecting boundary conditions for systems of conservation laws. We will concentrate on the equations of ideal magnetohydrodynamics (MHD) in a gravitationally balanced, stratified atmosphere. We will state the main results, discuss implementational aspects and show r sults in 1D and in 2D.

Keywords

Pressure Perturbation Absorb Boundary Condition Ghost Cell Riemann Solver Artificial Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bell JB, Colella P, and Trangenstein JA (1989): Higher Order Godunov Methods for General Systems of Hyperbolic Conservation Laws. J. Comput. Phys., 82: 362.MathSciNetMATHCrossRefGoogle Scholar
  2. Brie M, and Wu CC (1988): An Upwind Differencing Scheme for the Equations of Ideal Magnetohydrodynamics. J. Comput. Phys., 75: 400.MathSciNetCrossRefGoogle Scholar
  3. Dai W, Woodward PR (1995): A Simple Riemann Solver and High-Order Godunov Schemes for Hyperbolic Systems of Conservation Laws, J.Comput.Phys., 121: 51.MathSciNetMATHCrossRefGoogle Scholar
  4. Dedner A, Kröner D, Sofronov IL, Wesenberg M (2000): Transparent Boundary Conditions for MHD Simulations in Stratified Atmospheres, Preprint.Google Scholar
  5. Grote MJ, Keller JB (2000): Nonreflecting Boundary Conditions for Maxwell’s Equations, J.Comput.Phys., 139: 327.MathSciNetGoogle Scholar
  6. Kröner D (1991): Absorbing boundary conditions for the linearized Euler equations in 2-D, Math. Comput, 57: 153.MATHGoogle Scholar
  7. Sofronov IL (1998): Non -reflecting inflow and outflow in a wind tunnel for transonic time-accurate simulation, J.Math.Anal.Appl., 221: 92.MathSciNetMATHCrossRefGoogle Scholar
  8. Wesenberg M (2000) A Note on MHD Riemann Solvers. In preparation.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • A. Dedner
    • 1
  • D. Kröner
    • 1
  • M. Wesenberg
    • 1
  • I. Sofronov
    • 2
  1. 1.Institute for Applied MathematicsFreiburg UniversityGermany
  2. 2.Keldysh Institute of Applied Mathematics RASMoscowRussia

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