** Abstract.**

Accurate models of space weather need to resolve fast magnetic reconnection and strong shocks. The simplest such models known are Hall MHD and the more accurate two-fluid collisionless plasma model, which we have chosen for its conceptual and numerical simplicity. We seek to develop a fast 2D two-fluid solver for the GEM reconnection challenge problem. So far we have implemented and tested a 1D two-fluid shock-capturing finite volume solver. Our computations appear to verify that as a nondimensionalized Larmor radius approaches zero, our computed two-fluid solutions weakly approach the ideal MHD solution. To accelerate our methods we hope to selectively resolve fast waves only in regions where a fast phenomonon of interest (e.g., magnetic reconnection) is occuring, and elsewhere use a coarser time step, likely using adaptive mesh refinement (AMR) or implicit methods.

** Long version of abstract. **

The ability to model fast magnetic reconnection in space plasmas is critical to accurate modeling of solar flares and the interaction of the resulting coronal mass ejections with Earth's magnetosphere. Also critical in modeling such space weather is the ability to capture strong shocks.

The simplest and computationally least expensive known models which admit fast reconnection are a one-fluid model called Hall MHD and the more accurate two-fluid collisionless plasma model, which we have chosen for its conceptual and numerical simplicity.

Our goal is to develop a fast, shock-capturing two-dimensional method for two-fluid collisionless plasma that solves the GEM reconnection challenge problem. As an initial step, we have implemented and tested a shock-capturing finite volume solver for one-dimensional two-fluid collisionless plasma. Our computed solutions appear to verify that as a nondimensionalized Larmor radius approaches zero, two-fluid solutions weakly approach the ideal MHD solution.

Numerical models which resolve fast reconnection must resolve fast waves, which incurs computational expense due to the need for a short time step. Our strategy to accelerate our methods is to selectively resolve fast waves only in regions where a fast phenomonon of interest (e.g magnetic reconnection) is occuring, and elsewhere use a coarser time step. Two mechanisms which we are pursuing to stably take a larger time step are adaptive mesh refinement (AMR) and (semi-)implicit methods.