The Flash code was developed at the University of Chicago as part of the Department of Energy's Accelerated Strategic Computing Initiative (ASCI). The code was designed specifically to simulate thermonuclear flashes in compact stars (white dwarfs and neutron stars). This paper will give a brief introduction to the astrophysics problems we wish to address, followed by a description of the current version of the Flash code. Finally, we discuss two simulations of astrophysical detonations that we have carried out with the code. The first is of a helium detonation in an X-ray burst. The other simulation models a carbon detonation in a Type Ia supernova explosion. .