A semi-discrete central scheme for magnetohydrodynamics on orthogonalcurvilinear grids
This work describes a novel scheme for the equations of magnetohydrodynamics on orthogonalcurvilinear grids within a finite-volume framework. The scheme is based on a combination of central-upwind techniques for hyperbolic conservation laws and projectionevolution methods originally developed for HamiltonJacobi equations. The scheme is derived in semi-discrete form, and a full-fledged version is obtained by applying any stable and accurate solver for integration in time. The divergence-free condition of the magnetic field is a built-in property of the scheme by virtue of a constrained-transport ansatz for the induction equation. From the general formulation second-order accurate schemes for cylindrical grids and spherical grids are introduced in some more detail pointing out their potential importance in many applications. Special emphasis in this context is put to a treatment of the geometric axis implying severe complications because of the presence of coordinate singularities and associated grid degeneracy. An attempt to tackle these problems is presented. Numerical experiments illustrate the overall robustness and performance of the scheme for a small suite of tests.
magnetohydrodynamics numerics: central schemes