  A new approximate Riemann solver for the equations of magnetohydrodynamics
(MHD) with an isothermal equation of state is presented.
  The proposed method of solution draws on the recent work of
  Miyoshi and Kusano, in the context of adiabatic MHD, where an approximate
solution to the Riemann problem is sought in terms of an average constant
velocity and total pressure across the Riemann fan.
  This allows the formation of four intermediate states enclosed by two
outermost fast discontinuities and separated by two rotational waves and an
entropy mode.
  In the present work, a corresponding derivation for the isothermal
  MHD equations is presented.
  It is found that the absence of the entropy mode leads to a different
formulation which is based on a three-state representation rather than four.
  Numerical tests in one and two dimensions demonstrates that the new solver is
robust and comparable in accuracy to the more expensive linearized solver of
Roe, although considerably faster.

Astrophysics