Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However its relative efficiency increases in multidimensional simulations.Comment: 50 pages, 17 figures (2 in color). Submitted to ApJ Suppl. Se

On the application of Jacobian-free Riemann solvers for relativistic radiation magnetohydrodynamics under M1 closure

Radiative transfer plays a major role in high-energy astrophysics. In multiple scenarios and in a broad range of energy scales, the coupling between matter and radiation is essential to understand the interplay between theory, observations and numerical simulations. In this paper, we present a novel scheme for solving the equations of radiation relativistic magnetohydrodynamics within the parallel code L\'ostrego. These equations, which are formulated taking successive moments of the Boltzmann radiative transfer equation, are solved under the gray-body approximation and the M1 closure using an IMEX time integration scheme. The main novelty of our scheme is that we introduce for the first time in the context of radiation magnetohydrodynamics a family of Jacobian-free Riemann solvers based on internal approximations to the Polynomial Viscosity Matrix, which were demonstrated to be robust and accurate for non-radiative applications. The robustness and the limitations of the new algorithms are tested by solving a collection of one-dimensional and multi-dimensional test problems, both in the free-streaming and in the diffusion radiation transport limits. Due to its stable performance, the applicability of the scheme presented in this paper to real astrophysical scenarios in high-energy astrophysics is promising. In future simulations, we expect to be able to explore the dynamical relevance of photon-matter interactions in the context of relativistic jets and accretion discs, from microquasars and AGN to gamma-ray bursts.Comment: 21 pages, 13 figures. Accepted for publication in Computer Physics Communication