Application of a grid based hybrid finite volume/boundary element method for simulations of the kinematic induction equation with insulating boundary conditions.

The experimental realization of dynamo excitation as well as theoretical and numerical examinations of the induction equation have shown the relevance of boundary conditions and material properties for a self-sustaining dynamo. Generally, in non-spherical geometry typical insulating boundary conditions are described by elaborated schemes (e.g. solving of the Laplace equation in an extended domain) or by simplifying approximations (pseudo vacuum). A different approach is provided by a modified integral equation procedure, commonly known as the boundary element method (BEM). Integrating the Laplace equation on the boundaries allows to overcome the difficulties of the non-local character of insulating boundary conditions and the direct computation of the magnetic field next to an insulator becomes possible. However, 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.