A density-based method with semi-discrete central-upwind schemes for ideal magnetohydrodynamics

In the present work, the central-upwind schemes proposed by Kurganov et al. (SIAM J Sci Comput 23:707-740, 2001) for hydrodynamics are extended and combined with the divergence cleaning method of Dedner (J Comput Phys 175:645-673, 2002) in order to approximate the equations of the ideal magnetohydrodynamics in a finite volume discretization framework with Gaussian integration. To improve the quality of the solution, the Van Leer interpolation scheme is used. The accuracy and the robustness of the obtained solver are demonstrated through numerical simulations of benchmark problems such as the Brio-Wu shock tube problem, the Orszag-Tang vortex problem and the 2D cloud-shock interaction problem.