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The exact solution of the Riemann problem in relativistic magnetohydrodynamics with tangential magnetic fields. (English) Zbl 1083.76067
Summary: We have extended the procedure to find the exact solution of the Riemann problem in relativistic hydrodynamics to a particular case of relativistic magnetohydrodynamics in which the magnetic field of the initial states is tangential to the discontinuity and orthogonal to the flow velocity. The wave pattern produced after the break up of the initial discontinuity is analogous to the non-magnetic case, and we show that the problem can be understood as a purely relativistic hydrodynamical problem with a modified equation of state. The new degree of freedom introduced by the non-zero component of the magnetic field results in interesting effects consisting in the change of the wave patterns for given initial thermodynamical states, in a similar way to the effects arising from the introduction of tangential velocities. Secondly, when the magnetic field dominates the thermodynamical pressure and energy, the wave speeds approach the speed of light, leading to fast shocks and fast and arbitrarily thin rarefaction waves. Our approach is the first non-trivial exact solution of a Riemann problem in relativistic magnetohydrodynamics and it can also be of interest to test numerical codes against known analytical or exact solutions.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76L05 Shock waves and blast waves in fluid mechanics
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