Speaker: Robert K. Crockett, Dept. of Astronomy, UC Berkeley
The Interstellar Medium (ISM) can, to good approximation, be treated as non-resistive magnetized fluid. In order to accurately simulate this highly turbulent, compressible fluid requires numerical schemes that faithfully reproduce shocks and other nonlinear structures. These are handled very well in general by finite-volume Godunov methods. However, certain types of nonlinearities can cause problems wherein the divergence-free constraint, div.B=0, is not maintained. This can have deleterious effects, causing incorrect dynamics and field topologies, and numerical instabilities.
I outline several related Godunov schemes with for ensuring that the effects of not maintaining the divergence-free condition are minimized, even for highly nonlinear structures. All these schemes are based on an unsplit, second-order corner-transport upwind method. The schemes retain the cell-centering of variables, making extension to adaptive meshes easier. To this base scheme I have added steps that project non-solenoidal components from the magnetic field. Several test cases, including magnetized shocks and low beta flux tubes, are presented.