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We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show that the wave-pattern produced in a multidimensional relativistic Riemann problem can be predicted entirely by examining the initial conditions. Our method is logically very simple and allows for a numerical implementation of an exact Riemann solver which is both straightforward and computationally efficient. The simplicity of the approach is also important for revealing special relativistic effects responsible for a smooth transition from one wave-pattern to another when the tangential velocities in the initial states are suitably varied. While the content of this paper is focussed on a flat spacetime, the local Lorentz invariance allows its use also in fully general relativistic calculations.
A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general, when solvin
We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as we
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the flui
We have undertaken the simulation of hydrodynamic flows with bulk Lorentz factors in the range 10^2--10^6. We discuss the application of an existing relativistic, hydrodynamic primitive-variable recovery algorithm to a study of pulsar winds, and, in
A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity simulations