Numerical MHD Codes for Modeling Astrophysical Flows
  We describe a Godunov-type magnetohydrodynamic (MHD) code based on the
Miyoshi and Kusano (2005) solver which can be used to solve various
astrophysical hydrodynamic and MHD problems. The energy equation is in the form
of entropy conservation. The code has been implemented on several different
coordinate systems: 2.5D axisymmetric cylindrical coordinates, 2D Cartesian
coordinates, 2D plane polar coordinates, and fully 3D cylindrical coordinates.
Viscosity and diffusivity are implemented in the code to control the accretion
rate in the disk and the rate of penetration of the disk matter through the
magnetic field lines. The code has been utilized for the numerical
investigations of a number of different astrophysical problems, several
examples of which are shown.
