An integro-differential formulation
for magnetic induction in bounded domains:
Boundary Element--Finite Volume method
Alexey Iskakova, Stephane Descombesb,
Emmanuel Dormya,c
a IPGP, 4 place Jussieu, F-75252, Paris, France
b U.M.P.A., E.N.S. Lyon, 46 allée d'Italie,
69364 Lyon Cedex 07, France.
c C.N.R.S., France.
Journal of Computational Physics, 197, 540-554 (2004)
Abstract. Simulations of magnetohydrodynamic (MHD) flows in bounded domains
using spectral methods suffer from a number of serious limitations.
Alternative methods based on local discretisation raise the problem
of how to implement non-local boundary conditions for the magnetic field.
We have developed a new strategy for the numerical solution of
MHD problems in bounded domains, which combines the flexibility
of a local discretisation with a rigorous formulation of
magnetic boundary conditions next to an insulator in arbitrary geometries.
In accordance with the character of underlying equations
we apply a global integral approach at the boundary and
a differential approach inside the conducting domain.
The formulation of the boundary problem in terms of primitive variables
allows us to combine these approaches and propose a mixed
finite volume and boundary element method.
We illustrate its efficiency on magnetic diffusion problems
in a sphere and in a finite cylinder.
Key Words: Magnetohydrodynamics and electrohydrodynamics,
Hydrodynamic and hydromagnetic problems, Boundary element methods.