On the development of a rotated-hybrid HLL/HLLC approximate Riemann solver for relativistic hydrodynamics

Abstract

ABSTRACT This work presents the development of a rotated-hybrid Riemann solver for solving relativistic hydrodynamics (RHD) problems with the hybridization of the HLL and HLLC (or Rusanov and HLLC) approximate Riemann solvers. A standalone application of the HLLC Riemann solver can produce spurious numerical artefacts when it is employed in conjunction with Godunov-type high-order methods in the presence of discontinuities. It has been found that a rotated-hybrid Riemann solver with the proposed HLL/HLLC (Rusanov/HLLC) scheme could overcome the difficulty of the spurious numerical artefacts and presents a robust solution for the Carbuncle problem. The proposed rotated-hybrid Riemann solver provides sufficient numerical dissipation to capture the behaviour of strong shock waves for RHD. Therefore, in this work, we focus on two benchmark test cases (odd–even decoupling and double-Mach reflection problems) and investigate two astrophysical phenomena, the relativistic Richtmyer–Meshkov instability and the propagation of a relativistic jet. In all presented test cases, the Carbuncle problem is shown to be eliminated by employing the proposed rotated-hybrid Riemann solver. This strategy is problem-independent, straightforward to implement and provides a consistent robust numerical solution when combined with Godunov-type high-order schemes for RHD.