  Type Ia supernovae are bright stellar explosions distinguished by
standardizable light curves that allow for their use as distance indicators for
cosmological studies. Despite their highly successful use in this capacity, the
progenitors of these events are incompletely understood. We describe simulating
type Ia supernovae in the paradigm of a thermonuclear runaway occurring in a
massive white dwarf star. We describe the multi-scale physical processes that
realistic models must incorporate and the numerical models for these that we
employ. In particular, we describe a flame-capturing scheme that addresses the
problem of turbulent thermonuclear combustion on unresolved scales. We present
the results of our study of the systematics of type Ia supernovae including
trends in brightness following from properties of the host galaxy that agree
with observations. We also present performance results from simulations on
leadership-class architectures.
