Forward and inverse problems in fundamental and applied magnetohydrodynamics

TL;DR

This review discusses recent advances in solving forward and inverse problems in magnetohydrodynamics, focusing on numerical methods, experimental applications like the VKS dynamo, and flow reconstruction techniques such as CIFT.

Contribution

It provides a comprehensive overview of numerical schemes for induction processes and introduces practical applications of flow tomography in industrial and geophysical contexts.

Findings

Numerical treatment of induction processes in non-spherical domains.

CIFT effectively reconstructs flow fields in low magnetic Reynolds number flows.

Soft-iron impellers are crucial for the VKS dynamo operation.

Abstract

This Minireview summarizes the recent efforts to solve forward and inverse problems as they occur in different branches of fundamental and applied magnetohydrodynamics. As for the forward problem, the main focus is on the numerical treatment of induction processes, including self-excitation of magnetic fields in non-spherical domains and/or under the influence of non-homogeneous material parameters. As an important application of the developed numerical schemes, the functioning of the von-K\'{a}rm\'{a}n-sodium (VKS) dynamo experiment is shown to depend crucially on the presence of soft-iron impellers. As for the inverse problem, the main focus is on the mathematical background and some first practical applications of the Contactless Inductive Flow Tomography (CIFT), in which flow induced magnetic field perturbations are utilized for the reconstruction of the velocity field. The promises of CIFT for flow field monitoring in the continuous casting of steel are substantiated by results obtained at a test rig with a low melting liquid metal. While CIFT is presently restricted to flows with low magnetic Reynolds numbers, some selected problems of non-linear inverse dynamo theory, with possible application to geo- and astrophysics, are also discussed.