Martí et al. have used a version of Marquina’s method that applies the Lax–Friedrichs flux to all fields (modified Marquina’s flux formula) in their simulations of relativistic jets [182, 183]. 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 ). Numerical experimentation in two dimensions confirms that the dissipation of the scheme is sufficient to eliminate the carbuncle phenomenon , which appears in high Mach number relativistic jet simulations when using other standard solvers . 2D Simulations of relativistic AGN jets using Marquina’s flux formula have also been performed by Mizuta et al. , the code being second-order accurate in space (MUSCL reconstruction ) and first-order accurate in time. Aloy et al.  have implemented the modified Marquina flux formula in their three-dimensional relativistic hydrodynamic code GENESIS. Font et al.  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.
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