Numerical magetohydrodynamics in astrophysics: Algorithm and tests for one-dimensional flow`

Abstract

view Abstract Citations (223) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for One-dimensional Flow Ryu, Dongsu ; Jones, T. W. Abstract We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a nonlinear Riemann solver for ideal MHD, which includes rarefactions as well as shocks and produces exact solutions for two-dimensional magnetic field structures as well as for the three-dimensional ones. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (\ie ~one-dimensional flows) are presented. These include those for which the field structure is two-dimensional ({\it i.e.}, those flows often called ``$1 + 1/2$ dimensional'') as well as those for which the magnetic field plane rotates ({\it i.e.,}, those flows often called ``$1 + 1/2 + 1/2$ dimensional''). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within 2-4 cells while more cells are required if shocks become weak. With proper stiffening, rotational discontinuities are resolved within 3-5 cells. Contact discontinuities are also resolved within 3-5 cells with stiffening and 6-8 cells without stiffening, while the stiffening on contact discontinuities in some cases generates numerical oscillations. Tangential discontinuities spread over more than 10 cells. Our tests confirm that slow compound structures with two-dimensional magnetic field are composed of intermediate shocks (so called ``2-4'' Publication: The Astrophysical Journal Pub Date: March 1995 DOI: 10.1086/175437 arXiv: arXiv:astro-ph/9404074 Bibcode: 1995ApJ...442..228R Keywords: Algorithms; Computational Astrophysics; Magnetic Fields; Magnetohydrodynamics; One Dimensional Flow; Shock Waves; Computational Grids; Finite Difference Theory; Shock Tubes; Tvd Schemes; Upwind Schemes (Mathematics); Astrophysics; HYDROMAGNETICS; MAGNETOHYDRODYNAMICS: MHD; METHODS: NUMERICAL; SHOCK WAVES; Astrophysics E-Print: 32 pages with 14 figures (uuencoded compressed tar file of text and figures available via anonymous ftp from directory /pub at sirius.chungnam.ac.kr), submitted to The Astrophysical Journal, CNU-AST-94-1 full text sources arXiv | ADS |