A Flux-Split Algorithm Applied to Relativistic Flows

• Published in: Journal of computational physics Vol. 146; no. 1; pp. 58 - 81
• Main Authors: Donat, R., Font, J.A., Ibáñez, J.Ma, Marquina, A.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 10-10-1998
• Subjects: non-linear systems of conservation laws; shock capturing; special relativistic hydrodynamics
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1006/jcph.1998.5955

The equations of RFD 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, 42 (1996)) 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.