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RELAXATION SOLVERS FOR IDEAL MHD EQUATIONS-A REVIEW 被引量：1

RELAXATION SOLVERS FOR IDEAL MHD EQUATIONS-A REVIEW
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摘要 We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH. We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH.
作者 Christian Klingenberg Knut Waagan
机构地区 Departement of Mathematics The University of Maryland
出处 《Acta Mathematica Scientia》 SCIE CSCD 2010年第2期621-632,共12页 数学物理学报（B辑英文版）
关键词 conservation laws ideal magnetohydrodynamics finite volume schemes en-tropy stable schemes positive schemes conservation laws ideal magnetohydrodynamics finite volume schemes en-tropy stable schemes positive schemes
分类号 O361.3 [理学—流体力学]
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参考文献19

  • 1Audusse Emmanuel, Bouchut Franqois, Bristeau Marie-Odile, Klein Rupert, Perthame Benoit. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J Sci Comput, 2004, 25(6): 2050-2065.
  • 2Balsara Dinshaw S, Spicer Daniel S. A staggered mesh algorithm using high order Godunov fluxes to ensure solenodial magnetic fields in magnetohydrodynamic simulations. J Comput Phys, 1999. 149(2): 270-292.
  • 3Bouchut Francois. Nonlinear Stability of Finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in Mathematics. Basel: Birkhauser, 2004.
  • 4Bouchut Francois, Klingenberg Christian, Waagan Knut. A multiwave approximate Riemann solver for ideal MHD based on relaxation I - theoretical framework. Numerische Mathematik, 2007, 108(1): 7-41.
  • 5Bouchut Franqois, Klingenberg Christian, Waagan Knut. A multiwave approximate Riemann solver for ideal MHD based on relaxation II - numerical implementation with 3 and 5 waves. To appear in Numerische Mathematik, 2010.
  • 6Brackbill J U, Barnes D C. The effect of nonzero product of magnetic gradient and B on the numerical solution of the magnetohydrodynamic equations. J Comput Phys, 1980, 35:426--430.
  • 7Brio M, Wu C C. An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J Comput Phys, 1988, 75(2): 400-422.
  • 8Dedner A, Kemm F, Kroner D, Munz C -D, Schnitzer T, Wesenberg M. Hyperbolic divergence cleaning for the MHD equations. J Comput Phys, 2002, 175(2): 645-673.
  • 9Fryxell B, Olson K, Ricker P, Timmes F X, Zingale M, Lamb D Q, MacNeice P, Rosner R, Truran J W, Tufo H. Flash: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. The Astrophysical Journal Supplement Series, 2000, 131(1): 273-334.
  • 10Fuchs F, McMurry A, Mishra S, Risebro N H, Waagan K. Approximate Riemann-solver based High-order Finite Volume schemes for the Godunov-Powell form of the ideal MHD equations in multi-dimensions. Submitted.

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Acta Mathematica Scientia
2010年 第2期

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