Analytic models of heterogenous magnetic fields for liquid metal flow simulations

TL;DR

This paper presents a physically consistent method for modeling divergence- and curl-free inhomogeneous magnetic fields using simple analytical formulas, aiding simulations of liquid metal flows in magnetohydrodynamics.

Contribution

It introduces a new analytical approach to define external magnetic fields that are divergence- and curl-free, suitable for computational MHD studies involving inhomogeneous fields.

Findings

Analytical formulas for divergence- and curl-free magnetic fields.

Examples include peakwise, stepwise, shelfwise, and solenoid-induced fields.

Streamwise magnetic component significantly affects rapidly changing fields.

Abstract

A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be used in numerical studies where an inhomogeneous magnetic field influences a liquid metal flow. The resulting magnetic field is divergence and curl-free, and contains two components and parameters to vary. As an illustration, the following examples are considered: peakwise, stepwise, shelfwise inhomogeneous magnetic fields, and the field induced by a solenoid. Finally, the impact of the streamwise magnetic field component is shown qualitatively to be significant for rapidly changing fields.