(untitled) (Communications in Computational Physics, 2008)
We consider whether implicit simulation techniques can be extended in time and space scales to magnetohydrodynamics without any change but the addition of collisions. Our goal is to couple fluid and kinetic models together for application to multi-scale problems. Within a simulation framework, transition from one model to the other would occur not by a change of algorithm, but by a change of parameters. This would greatly simplify the coupling. Along the way, we have found new ways to impose consistent boundary conditions for the field solver that result in charge and energy conservation, and establish that numerically-generated stochastic heating is the problem to overcome. For an MHD-like problem, collisions are clearly necessary to reduce the stochastic heating. Without collisions, the heating rate is unacceptable. With collisions, the heating rate is significantly reduced.