Finite difference weighted essentially non-oscillatory schemes with constrained transport for 2D ideal Magnetohydrodynamics

Summary form only given. A novel algorithm based on a high order finite difference adaptive WENO scheme [2] will be presented to solve the 2D ideal Magnetohydrodynamics (MHD) equations. The algorithm will use the unstaggered Constrained Transport technique from the magnetic potential advection constrained transport method [2] to satisfy the divergence-free constraint of the magnetic field. However the treatment of our algorithm is significantly different from [2]. The new feature will be (1) the method is finite difference type, (2) high order in both time (4^th-order) and space (3^rd-order), (3) all the conservative quantities are essentially non-oscillatory, (4) Adaptive Mesh Refinement will be used as the base framework to increase resolution. Convergence study will be done on the smooth problem. 2D/2.5D benchmark problems such as rotated Brio-Wu shock tube, Orszag-Tang and Cloud-shock interaction will be presented. We expect our algorithm is robust, essentially non-oscillatory and can capture shock waves and discontinuities well.