Numerical simulation of flux expulsion in a plain channel MHD flow

Numerical simulation of forced magnetohydrodynamic (MHD) channel flow is performed under conditions where the magnetic Reynolds number is comparable to or significantly exceeds 1. The dimensionless parameters of the problem, used for verification, correspond to flow regimes characterized by the complex MHD interaction between the flow and the magnetic field. The aim of this work is to verify and analyze the performance and accuracy of numerical simulation software packages COMSOL Multiphysics, ANES, OpenFOAM, and Elmer in application to two different formulations of the considered problem: one written in terms of the induced magnetic field, and the other in terms of the magnetic vector potential. The results of the author's calculations are compared with the results from the approximate analytical solution for a one-dimensional formulation and with those from other authors. A comparative analysis indicates the key role of a nonlinear term in the equation of motion, which correctly models the phenomenon of hydraulic resistance crisis during the transition from Hartmann flow to Poiseuille flow. Neglecting this term leads to significant errors in the representation, especially, of unsteady Poiseuille flow. The computational experiments conducted by the authors, as well as those known from literature sources, show that the models of all software packages tested in this work are capable of reproducing the main flow patterns; however, the highest accuracy is achieved with strict adherence to the Courant criterion. The model implemented in OpenFOAM demonstrates values especially close to the published values in the Poiseuille regime. In terms of computational efficiency, the best performance is shown by the OpenFOAM system (open-source) and the freely distributed ANES, both implemented using the finite volume method. The finite element models of COMSOL and Elmer packages are characterized by longer computation time and lower parallelization efficiency. Based on the obtained results, one can select software packages that are best suited for numerical simulation of specific unsteady MHD flows in fusion-related problems.