A high-resolution constrained transport method with adaptive mesh refinement for ideal MHD Original Research Article

We consider a high-resolution finite volume method that utilizes a constrained transport technique to keep the magnetic field divergence-free. This scheme is based on the wave propagation method of LeVeque [J. Comp. Phys. 131 (1997) 327] and makes use of the constrained transport framework of Evans and Hawley [Astrophys. J. 332 (1988) 659]. This method differs from other constrained transport methods in that it is based on directly solving the magnetic potential equation in conjunction with a special limiting strategy to obtain a non-oscillatory magnetic field. It is formulated without the use of a staggered grid and implemented so that no spatial averaging is needed in the update. We present in this work an adaptive mesh refinement implementation of this method using the amrclaw software package developed by Berger and LeVeque [SIAM J. Numer. Anal. 35 (1998) 2298]. The proposed method is tested on a two-dimensional cloud-shock interaction problem.