Tensor-product-Thomas elliptic solver for liquid-metal magnetohydrodynamics

Abstract

A new approach to numerical simulation of magnetohydrodynamic flows of liquid metals is presented. It combines the conservative finite-difference discretization with a tensor-product-Thomas solution of the elliptic problems for pressure, electric potential, velocity, and temperature. The method is realizable on an arbitrarily clustered structured grid. The main novelty of the approach is the efficient solution of the practically important and computationally challenging elliptic problems for electric potential in flow domains with thin electrically conducting walls. The method is verified via solution of benchmark problems for streamwise-uniform and nonuniform, steady and unsteady magnetohydrodynamic flows in ducts, and for thermal convection in boxes of various aspect ratios. Computational efficiency of the method in comparison to the existing ones is demonstrated.