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

Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in theclass of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewiseparabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe andHarten–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 relativisticmagnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quitecomplex and does not have an analytical solution. The present paper proposes the development ofRusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in theequations of special relativistic magnetohydrodynamics. The developed scheme was verified usingeight classical problems on the decay of an arbitrary discontinuity that describe the main featuresof relativistic magnetized flows.