A central differencing simulation of the Orszag-Tang vortex system

The Orszag-Tang vortex system describes the transition to supersonic turbulence for the equations of magnetohydrodynamics (MHD) in two space dimensions. The complex interaction between various shock waves traveling at different speed regimes that characterizes the solution of this test problem requires the use of numerical schemes capable of detecting and resolving accurately steep gradients while avoiding the onset of spurious oscillations. A simulation of the Orszag-Tang MHD vortex system computed with a third-order semi-discrete central scheme (Kurganov and Tadmor, 2000), (Balbas and Tadmor, submitted to SIAM Journal of Scientific Computing) is presented below. The central differencing approach avoids any detailed knowledge of the characteristic structure of the hyperbolic model, resulting in simple to implement, yet robust, black-box numerical schemes, (Balbas and Tadmor, 2004).