A checkerboard-free symmetry-preserving conservative method for magnetohydrodynamic flows

Abstract

Simulating MHD flows at high Hartmann numbers and low magnetic Reynolds numbers is of high interest for the design of a nuclear fusion breeding blanket, for which high accuracy and conservation of physical properties are of great importance. In this work, a solver is developed that offers these properties through the symmetry-preserving method, while at the same time warranting unconditional stability. Since this method uses predictor values for the pressure and electric potential fields, it can be prone to checkerboarding. Therefore it is extended to include a dynamical checkerboarding solution, which balances this problem with numerical dissipation. This is done through run-time measurements of the intensity of checkerboarding, which is then used as a negative feedback onto the predictor values. The symmetry-preserving discretisation and the dynamical solution to checkerboarding were successfully tested using an magnetohydrodynamic Taylor-Green vortex. The newly introduced method shows results free from numerical dissipation in smooth cases, whereas it avoids checkerboarding in more challenging cases. Finally, the method shows to be unconditionally stable, even on highly distorted meshes.