A positive MUSCL–Hancock scheme for ideal magnetohydrodynamics
Abstract: We present a second order accurate scheme for the Euler equations and the ideal MHD equations that ensures positivity of mass density and pressure. The scheme is of predictor-corrector type, with a MUSCL scheme following as a special case. The crucial steps are to limit the spatial reconstruction (and hence the prediction step) in a precise manner, and, for MHD, to include Powell terms in an appropriate discrete form. The numerical examples show that the scheme has superior stability compared to more basic schemes, while maintaining accuracy.