  We have built a code to obtain the exact solutions of Riemann problems in
ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code
can handle not only regular waves but also switch-on/off rarefactions and all
types of non-regular shocks: intermediate shocks and switch-on/off shocks.
Furthermore, the initial conditions with vanishing normal or transverse
magnetic fields can be handled although the code is partly based on the
algorithm proposed by Torrilhon (2002) (Torrilhon 2002 Exact Solver and
Uniqueness Condition for Riemann problems of Ideal Magnetohydrodynamics.
Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich), which
cannot deal with all types of non-regular waves nor the initial conditions
without normal or transverse magnetic fields. Our solver can find all the
solutions for a given Riemann problem and hence, as demonstrated in this paper,
one can investigate the structure of the solution space in detail. Therefore
the solver is a powerful instrument to solve the outstanding problem of the
existence and uniqueness of solutions of MHD Riemann problems. Moreover, the
solver may be applied to numerical MHD schemes like the Godunov scheme in the
future.
