A hybrid finite volume - boundary element method (FV-BEM) for the numerical solution of the kinematic induction equation

The experimental realization of dynamo excitation has demonstrated the relevance of boundary conditions and material properties for a self-sustaining dynamo. The consideration of conductivity or permeability inhomogeneities requires a flexible numerical method that utilizes a local discretization scheme. A fast and accurate approach is provided by the constraint transport (CT) approach, a well known realization of a finite volume (FV) method that intrinsically maintains the solenoidal character of the magnetic field. The
problem of laboratory boundary conditions is treated by the boundary element method (BEM) which in combination with the FV scheme offers the flexibility of a local discretization with a stringent treatment of insulating magnetic boundary conditions.

Test simulations reproduce key results of the induction effects of a von-Karman-like flow and demonstrate the applicability and reliability of the approach.

Current examinations investigate the dynamo process presented by Busse & Wicht (1992, GaFD, 64, 135-144) who showed that a constant flow over a conducting material that exhibits a sinusoidal variation of the conductivity is already sufficient to generate a dynamo.