An efficient shock-capturing central-type scheme for multidimensional relativistic flows
Dipartimento di Astronomia e Scienza dello Spazio, Università degli Studi di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy
Corresponding author: L. Del Zanna, firstname.lastname@example.org
Accepted: 22 May 2002
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 to the consequent complexity of the Jacobian matrices (needed for the spectral decomposition in most of the approximate Riemann solvers of common use). Here an efficient and easy-to-implement three-dimensional (3-D) shock-capturing scheme for ideal RHD is presented. Based on the algorithms developed by P. Londrillo & L. Del Zanna (2000, ApJ, 530, 508) for the non-relativistic magnetohydrodynamic (MHD) case, and having in mind its relativistic MHD extension (to appear in a forthcoming paper), 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.
Key words: hydrodynamics / relativity / shock waves / methods: numerical
© ESO, 2002