We discuss the challenges of modeling X-ray bursts in multi-dimensions, review the different calculations done to date, and discuss our new set of ongoing simulations. We also describe algorithmic improvements that may help in the future to offset some of the expense of these simulations, and describe what may be possible with exascale computing.

We describe the AMReX suite of astrophysics codes and their application to modeling problems in stellar astrophysics. Maestro is tuned to efficiently model subsonic convective flows while Castro models the highly compressible flows associated with stellar explosions. Both are built on the block-structured adaptive mesh refinement library AMReX. Together, these codes enable a thorough investigation of stellar phenomena, including Type Ia supernovae and X-ray bursts. We describe these science applications and the approach we are taking to make these codes performant on current and future many-core and GPU-based architectures.