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Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic

Patryk Mach¹, Małgorzata Pietka

¹M Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 21, 2010

Abstract:

We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the ultrarelativistic equation of state (the pressure being directly proportional to the energy density) allows us to express this solution in analytical terms. The result can be used both to construct and test numerical schemes for relativistic Euler equations in (3+1) dimensions.

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