A HIGH ORDER FINITE DIFFERENCE WEIGHTED ESSENTIALLY NONOSCILLATORY SCHEME WITH A KERNEL-BASED CONSTRAINED TRANSPORT METHOD FOR IDEAL MAGNETOHYDRODYNAMICS

The ideal magnetohydrodynamics equations are challenging because one needs to maintain the divergence-free condition, del center dot B = 0. Many numerical methods have been developed to enforce this condition. In this paper, we extend our work on mesh aligned constrained transport by developing a new approach for the vector potential in two and three dimensions. The approach for solving the vector potential is based on the method of lines transpose and is A-stable, eliminating the need for diffusion limiters needed in our previous work in three dimensions. For problems with strong shocks, this approach offers considerable improvements when compared with our previous version of constrained transport. The method is robust and has been tested on the 2D and 3D cloud shock, blast wave, and field loop problems.