Magnetic field computations require a divergence cleaning step which is carried out here by solving a Poisson equation for the correction over the entire grid hierarchy using the fast-multipole method (FMM). The use of FMM will also allow us to treat self-gravity and diffusion problems in a straightforward way in the future. For hydrodynamics we use a full non-linear Riemann solver while for MHD an approximate Riemann solver is invoked. In both cases wave propagation algorithms are used for updates of finite volume values. We present a series of calculations and tests which demonstrate AstroBEAR's capabilities. These include simulations of strongly cooling interstellar bullets and "clumpy flows" (shocks interacting with multiple clumps). We also present simulations of a hypersonic jet in a cross wind applicable to laboratory astrophysics experiments and 3-D simulations of jets colliding/interacting in the context of dense clusters. Finally we present test calculations of our MHD version of the code.
Particular emphasis is placed on our clumpy flow studies as these highlight the utility of AMR and our approach to it. While strongly cooling heterogeneous flows are ubiquitous in astrophysics their complexity has kept them relatively unexplored both analytically and numerically. Using AstroBEAR we are carrying forward a systematic study of the properties of "radiative" clumpy flows and our results shed new light and their importance for mixing, mass loading and the transitions of astrophysical flows to turbulence. We present both 2-D and 3-D studies as an example of AstroBEAR's dimensional flexibility and the source term modularity