RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

Abstract

We obtain renormalized sets of right and left eigenvectors of the flux vector\nJacobians of the relativistic MHD equations, which are regular and span a\ncomplete basis in any physical state including degenerate ones. The\nrenormalization procedure relies on the characterization of the degeneracy\ntypes in terms of the normal and tangential components of the magnetic field to\nthe wavefront in the fluid rest frame. Proper expressions of the renormalized\neigenvectors in conserved variables are obtained through the corresponding\nmatrix transformations. Our work completes previous analysis that present\ndifferent sets of right eigenvectors for non-degenerate and degenerate states,\nand can be seen as a relativistic generalization of earlier work performed in\nclassical MHD. Based on the full wave decomposition (FWD) provided by the the\nrenormalized set of eigenvectors in conserved variables, we have also developed\na linearized (Roe-type) Riemann solver. Extensive testing against one- and\ntwo-dimensional standard numerical problems allows us to conclude that our\nsolver is very robust. When compared with a family of simpler solvers that\navoid the knowledge of the full characteristic structure of the equations in\nthe computation of the numerical fluxes, our solver turns out to be less\ndiffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The\namount of operations needed by the FWD solver makes it less efficient\ncomputationally than those of the HLL family in one-dimensional problems.\nHowever its relative efficiency increases in multidimensional simulations.\n