Positivity-preserving WENO schemes with constrained transport for ideal magnetohydrodynamic equations

Summary form only given. A novel positivity-preserving flux limiting technique is developed for finite difference WENO schemes to solve the idea magnetohydrodynamic (MHD) equations. The key challenges in applying such methods to ideal MHD are not only maintaining the positivity of density and pressure but also controlling divergence errors in the magnetic field. These two requirements are fulfilled by two steps: first implementing positivity-preserving flux limiter on the base WENO solver and then correcting the magnetic field and the total energy by a high-order constrained transport approach that is based on evolving the magnetic potential. Several 1D, 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to demonstrate the importance and efficiency to maintain the positivity of the solution of test problems including low-beta plasma flows.