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 [183
]). Numerical
experimentation in two dimensions confirms that the dissipation of
the scheme is sufficient to eliminate the carbuncle
phenomenon [238], which appears in high
Mach number relativistic jet simulations when using other standard
solvers [75
]. 2D Simulations of
relativistic AGN jets using Marquina’s flux formula have also been
performed by Mizuta et al. [196], the code being
second-order accurate in space (MUSCL reconstruction [282
]) and first-order
accurate in time. Aloy et al. [6
] have implemented
the modified Marquina flux formula in their three-dimensional
relativistic hydrodynamic code GENESIS. Font et al. [93
] 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.