MODERN NUMERICAL SCHEMES FOR SOLVING MAGNETOHYDRODYNAMIC EQUATIONS

In this paper several modern shock-capturing schemes for solving hydro dynamic and magnetohydrodynamic equations are reviewed. This review co vers a wide range of explicit and implicit schemes as well as those in which adaptive mesh refinement methods are adopted. As these numerica l schemes are based on Riemann solvers which use Godunov-type techniqu es, they are well suited for strong shocks and other discontinuities w ithout oscillations in the flow variables. Some other numerical issues as grid generation, divergence cleaning, and an application of MHD sc hemes to several problems in coronal and interplanetary physics are di scussed.