A Multi-Dimensional Magnetohydrodynamic Code in Cylindrical Geometry

Statistics – Computation

Scientific paper

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Hydromagnetics, Magnetohydrodynamics: Mhd, Methods: Numerical, Shock Waves

Scientific paper

We describe the implementation of a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics(MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, calld the Total Variation Diminishing (TVD) scheme, which is a second-order accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.

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