Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Programming the Boundary Element Method
Programming the Boundary Element Method
The integral equation method for a steady kinematic dynamo problem
Journal of Computational Physics
An interior penalty Galerkin method for the MHD equations in heterogeneous domains
Journal of Computational Physics
Spectral method for matching exterior and interior elliptic problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
Simulations of magnetohydrodynamic (MHD) flows in bounded domains using spectral methods suffer from a number of serious limitations. Alternative methods based on local discretization 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 discretization 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.