Accurate and Robust Pressure Weight Advection Upstream Splitting Method for Magnetohydrodynamics Equations

This research was supported by National Space Laboratory (NSL: S10801000121-08A0100-12110) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science, and Technology.

[1]  Andreas Dedner.  Solving the system of Radiation Magnetohydrodynamics: for solar physical simulations in 3d , 2009 .

[2]  C. Richard DeVore,et al.  Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics , 1989 .

[3]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[4]  Chongam Kim,et al.  Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows Part I Spatial discretization , 2005 .

[5]  W. Habashi,et al.  A finite element method for magnetohydrodynamics , 2001 .

[6]  J. Brackbill,et al.  The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations☆ , 1980 .

[7]  S. Orszag,et al.  Small-scale structure of two-dimensional magnetohydrodynamic turbulence , 1979, Journal of Fluid Mechanics.

[8]  G. Tóth.  The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes , 2000 .

[9]  Kun Xu,et al.  A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics , 2000 .

[10]  C. Munz,et al.  Hyperbolic divergence cleaning for the MHD equations , 2002 .

[11]  Oh-Hyun Rho,et al.  Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme , 2001 .

[12]  Gérard Gallice,et al.  Roe Matrices for Ideal MHD and Systematic Construction of Roe Matrices for Systems of Conservation Laws , 1997 .

[13]  K. Hoffmann,et al.  Numerical Solution of the Ideal Magnetohydrodynamic Equations for a Supersonic Channel Flow , 1998 .

[14]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

[15]  C. Munz,et al.  Lagrangian and Symmetry Structure of the Divergence Cleaning Model Based on Generalized Lagrange Multipliers , 2004 .

[16]  M. Liou.  A Sequel to AUSM , 1996 .

[17]  P. Roe,et al.  A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics , 1999 .

[18]  Phillip Colella,et al.  A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics , 1994, SIAM J. Sci. Comput..

[19]  J. Steger,et al.  Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods , 1981 .

[20]  Dinshaw S. Balsara,et al.  Linearized Formulation of the Riemann Problem for Adiabatic and Isothermal Magnetohydrodynamics , 1998 .

[21]  John Lyon,et al.  A time dependent three‐dimensional simulation of the Earth's magnetosphere: Reconnection events , 1982 .

[22]  T. Linde,et al.  A three-dimensional adaptive multifluid MHD model of the heliosphere. , 1998 .

[23]  Steven J. Plimpton,et al.  Nonlinear magnetohydrodynamics simulation using high-order finite elements , 2004 .

[24]  Katharine Gurski,et al.  An HLLC-Type Approximate Riemann Solver for Ideal Magnetohydrodynamics , 2001, SIAM J. Sci. Comput..

[25]  A. Ferrari,et al.  PLUTO: A Numerical Code for Computational Astrophysics , 2007, astro-ph/0701854.

[26]  James A. Rossmanith.  A high-resolution constrained transport method with adaptive mesh refinement for ideal MHD , 2004, Comput. Phys. Commun..

[27]  M. Brio,et al.  An upwind differencing scheme for the equations of ideal magnetohydrodynamics , 1988 .

[28]  N. Aslan,et al.  NUMERICAL SOLUTIONS OF ONE–DIMENSIONAL MHD EQUATIONS BY A FLUCTUATION APPROACH , 1996 .

[29]  Dongsu Ryu,et al.  Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow , 1995 .

[30]  J. Hawley,et al.  Simulation of magnetohydrodynamic flows: A Constrained transport method , 1988 .

[31]  Paul R. Woodward,et al.  Extension of the Piecewise Parabolic Method to Multidimensional Ideal Magnetohydrodynamics , 1994 .

[32]  Jiang-feng Wang,et al.  Upwind Scheme for Ideal 2-D MHD Flows Based on Unstructured Mesh , 2007 .

[33]  James A. Rossmanith,et al.  An Unstaggered, High-Resolution Constrained Transport Method for Magnetohydrodynamic Flows , 2006, SIAM J. Sci. Comput..

[34]  Shengtai Li.  An HLLC Riemann solver for magneto-hydrodynamics , 2005 .

[35]  K. Kusano,et al.  A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics , 2005 .

[36]  P. Janhunen,et al.  A Positive Conservative Method for Magnetohydrodynamics Based on HLL and Roe Methods , 2000 .