  Type Ia supernovae (SNe Ia) are the largest thermonuclear explosions in the
Universe. Their light output can be seen across great distances and has led to
the discovery that the expansion rate of the Universe is accelerating. Despite
the significance of SNe Ia, there are still a large number of uncertainties in
current theoretical models. Computational modeling offers the promise to help
answer the outstanding questions. However, even with today's supercomputers,
such calculations are extremely challenging because of the wide range of length
and time scales. In this paper, we discuss several new algorithms for
simulations of SNe Ia and demonstrate some of their successes.
