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A flux-split algorithm applied to relativistic flows. (English) Zbl 0930.76054
Summary: The equations of relativistic fluid dynamics can be written as a hyperbolic system of conservation laws by choosing an appropriate vector of unknowns. We give an explicit formulation of the full spectral decomposition of the Jacobian matrices associated with the fluxes in each spatial direction, which is the essential ingredient of the techniques we propose in this paper. These techniques are based on the recently derived flux formula of Marquina, a new way to compute the numerical flux at a cell interface which leads to a conservative, upwind numerical scheme. Using the spectral decompositions in a fundamental way, we construct high order versions of the basic first-order scheme described by R. Donat and A. Marquina in [J. Comput. Phys. 125, No. 1, 42-58, Art. No. 0078 (1996; Zbl 0847.76049)] and test their performance in several standard simulations in one dimension. Two-dimensional simulations include a wind tunnel with a flat faced step and a supersonic jet stream, both of them in strongly ultrarelativistic regimes. $$\copyright$$ Academic Press.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76M22 Spectral methods applied to problems in fluid mechanics 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 83-08 Computational methods for problems pertaining to relativity and gravitational theory
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