An E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices. [DOI:10.1016/j.jcp.2012.04.015]

The article was published as:
Shen YQ; Zha GC; Huerta MA. E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme. JOURNAL OF COMPUTATIONAL PHYSICS, 231(19):6233-6247(2012)