Abstract
We present a new high-order method for the unsteady viscous MHD equations in two and three dimensions. The two main features of this method are: (1) the discontinuous Galerkin projections for both the advection and diffusion components, and (2) the polymorphic spectral/hp elements for unstructured and hybrid discretizations. An orthogonal spectral basis written in terms of Jacobi polynomials is employed, which results in a matrix-free algorithm and thus high computational efficiency. We present several results that document the high-order accuracy of the method and perform a systematic p-refinement study of the compressible Orszag–Tang vortex as well as simulations of plasma flow past a circular cylinder. The proposed method, which can be thought of as a high-order extension of the finite volume technique, is suitable for direct numerical simulations of MHD turbulence as well as for other traditional MHD applications.
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