Using Piecewise Parabolic Reconstruction of Physical Variables in Rusanov’s Solver. II. Special Relativistic Magnetohydrodynamics Equations

Abstract

Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in the class of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewise parabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe and Harten–Lax–Van Leer solvers when using a similar reconstruction. Moreover, unlike these solvers, the numerical solution is free from artifacts. In the case of equations of special relativistic magnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quite complex and does not have an analytical solution. The present paper proposes the development of Rusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in the equations of special relativistic magnetohydrodynamics. The developed scheme was verified using eight classical problems on the decay of an arbitrary discontinuity that describe the main features of relativistic magnetized flows.