Martí et al. have used this method in their simulations of relativistic jets [110, 111]. The resulting numerical code has been successfully used to describe ultra-relativistic flows in both one and two spatial dimensions with great accuracy (a large set of test calculations using Marquina's Riemann solver can be found in Appendix II of [111]). Numerical experimentation in two dimensions confirms that the dissipation of the scheme is sufficient to eliminate the carbuncle phenomenon [153], which appears in high Mach number relativistic jet simulations when using other standard solvers [43].

Aloy et al. [3] have implemented Marquina's flux formula in their three dimensional relativistic hydrodynamic code GENESIS.

Font et al. [59] have developed a 3D general relativistic hydro code where the matter equations are integrated in conservation form and fluxes are calculated with Marquina's formula.

Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
http://www.livingreviews.org/lrr-1999-3
© Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |