The space-time CE/SE method for solving one-dimensional special relativistic magnetohydrodynamics equations

The development of powerful computational tools for simulating phenomena that inhibits the relativistic magnetohydrodynamic (MHD) structure has become one of the core research issues in astrophysics and is one of the compelling fields. The relativistic MHD equations are more complex than the non-relativistic ones due to non-linear relations between conserved and state (primitive) variables. The non-linearity of the systems and the flow near speed of light pose major challenges to the theoretical investigation of the models and to the numerical solution techniques. The current numerical study is related to the implementation of the space-time conservation element and solution element (CE/SE) method for solving one-dimensional special relativistic magnetohydrodynamic (SRMHD) equations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building blocks of the suggested method. The method differs from previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation. For validation, the numerical results of the method are compared with the second order central and kinetic flux-vector splitting schemes. The one-dimensional computations of this paper verify the method's efficiency, robustness and accuracy which are the key parameters in the context of astrophysical scenario.