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

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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

A new approach combining conservative finite-difference discretization with a tensor-product-Thomas solution is proposed for numerical simulation of magnetohydrodynamic flows of liquid metals. The method efficiently solves the important elliptic problems for electric potential in flow domains with thin electrically conducting walls. Its effectiveness is demonstrated through benchmark problems and compared favorably to existing methods in terms of computational efficiency. (c) 2022 Elsevier Inc. All rights reserved.