A new hybrid numerical scheme for two-dimensional ideal MHD equations

We present a new hybrid numerical scheme for two-dimensional (2D) ideal magnetohydrodynamic (MHD) equations. A simple conservation element and solution element (CESE) method is used to calculate the flow variables, and the unknown first-order spatial derivatives involved in the CESE method are computed with a finite volume scheme that uses the solution of the derivative Riemann problem with limited reconstruction to evaluate the numerical flux at cell interface position. To show the validation and capacity of its application to 2D MHD problems, we study several benchmark problems. Numerical results verify that the hybrid scheme not only performs well, but also can retain the solution quality even if the Courant number ranges from close to 1 to less than 0.01.