An adaptive moving mesh method for two-dimensional relativistic magnetohydrodynamics

This paper develops an adaptive moving mesh method for two-dimensional ideal relativistic magnetohydrodynamical (RMHD) equations that utilizes the initial reconstruction of the primitive variables in the logical domain and the projection technique for the solenoidal constraint of the magnetic field. The method consists of two “independent” parts: the time evolution of the RMHD equations and the mesh iteration redistribution. In the first part, the RMHD equations are solved on a fixed quadrangular mesh by using a high-resolution shock-capturing scheme. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical experiments are carried out to demonstrate the accuracy and effectiveness of the proposed method.

Highlight► A moving mesh method is first proposed for 2D relativistic magnetohydrodynamics. ► The method is easy implemented by two “independent” parts. ► Initial reconstruction of primitive variables is used to save the computational cost. ► Projection technique and AMG method are used for the solenoidal constraint. ► Accuracy and effectiveness of the method are demonstrated by numerical experiments.