A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics
We present a highly robust second order accurate scheme for the Euler equations and the ideal MHD equations. The scheme is of predictorcorrector type, with a MUSCL scheme following as a special case. The crucial ingredients are an entropy stable approximate Riemann solver and a new spatial reconstruction that ensures positivity of mass density and pressure. For multidimensional MHD, a new discrete form of the Powell source terms is vital to ensure the stability properties. The numerical examples show that the scheme has superior stability compared to standard schemes, while maintaining accuracy. In particular, the method can handle very low values of pressure (i.e. low plasma ? ? or high Mach numbers) and low mass densities.
magnetohydrodynamics finite volume methods positive conservative schemes