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We have built a code to obtain the exact solutions of Riemann problems inideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The codecan handle not only regular waves but also switch-on/off rarefactions and alltypes of non-regular shocks: intermediate shocks and switch-on/off shocks.Furthermore, the initial conditions with vanishing normal or transversemagnetic fields can be handled although the code is partly based on thealgorithm proposed by Torrilhon (2002) (Torrilhon 2002 Exact Solver andUniqueness Condition for Riemann problems of Ideal Magnetohydrodynamics.Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich), whichcannot deal with all types of non-regular waves nor the initial conditionswithout normal or transverse magnetic fields. Our solver can find all thesolutions for a given Riemann problem and hence, as demonstrated in this paper,one can investigate the structure of the solution space in detail. Thereforethe solver is a powerful instrument to solve the outstanding problem of theexistence and uniqueness of solutions of MHD Riemann problems. Moreover, thesolver may be applied to numerical MHD schemes like the Godunov scheme in thefuture.

Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves