Kinematic simulations of dynamo action with a hybrid boundary-element/finite-volume method

TL;DR

This paper presents a hybrid finite volume-boundary element method for simulating dynamo action, effectively handling complex geometries and boundary conditions, and demonstrates its reliability through kinematic simulations.

Contribution

It introduces a novel hybrid FV-BEM approach for dynamo simulations, combining local discretization with accurate boundary condition treatment in complex geometries.

Findings

The hybrid method accurately simulates dynamo action with prescribed flows.

The approach is computationally efficient for complex geometries.

Reliability confirmed through kinematic simulation results.

Abstract

The experimental realization of dynamo excitation as well as theoretical and numerical examinations of the induction equation have shown the relevance of boundary conditions for a self-sustaining dynamo. Within the interior of a field producing domain geometric constraints or varying material properties (e.g. electrical conductivity of the container walls or localized high-permeability material) might also play a role. Combining a grid based finite volume approach with the boundary element method in a hybrid FV-BEM scheme offers the flexibility of a local discretization with a stringent treatment of insulating magnetic boundary conditions in almost arbitrary geometries at comparatively low costs. Kinematic simulations of dynamo action generated by a well known prescribed mean flow demonstrate the reliability of the approach. Future examinations are intended to understand the behavior of the VKS-dynamo experiment where the field producing flow is driven by ferrous propellers and the induction effects of conductivity/permeability inhomogeneities might provide the required conditions for the measured dynamo characteristics.