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An efficient shoch-capturing central-type scheme for multidimensional relativistic flows. (English) Zbl 1209.76022
Summary: Multidimensional shock-capturing numerical schemes for special relativistic hydrodynamics (RHD) are computationally more expensive than their correspondent Euler versions, due to the nonlinear relations between conservative and primitive variables and due to the consequent complexity of Jacobian matrices (needed for spectral decomposition in most of the approximate Riemann solvers of common use). Here an efficient and easy-to-implement three-dimensional shock-capturing scheme for ideal RHD is presented. Based on the algorithms developed for the non-relativistic magnetohydrodynamic (MHD) case, and having in mind its relativistic MHD extension, the scheme uses high-order (third) convex essentially non-oscillatory (CENO) finite difference interpolation routines and central-type averaged Riemann solvers, which do not make use of time-consuming characteristic decomposition. The scheme is very efficient and robust, and it gives results comparable to those obtained with more sophisticated algorithms, even in ultrarelativistic multidimensional test problems.

76M20 Finite difference methods applied to problems in fluid mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76L05 Shock waves and blast waves in fluid mechanics
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