Integral equations in MHD: theory and application
Frank Stefani, Mingtian Xu, Gunter Gerbeth, and Thomas Wondrak
TL;DR
This paper discusses the formulation of the induction equation in magnetohydrodynamics as integral equations, highlighting recent numerical methods and their applications to dynamo theory and applied MHD problems.
Contribution
It introduces a unified integral equation approach for MHD, enabling advanced numerical solutions for forward and inverse dynamo problems.
Findings
Development of numerical schemes for integral equations in MHD
Application to dynamo theory problems
Enhanced understanding of magnetic field behavior in fluids
Abstract
The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD.
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