  Thermonuclear (type Ia) supernovae are bright stellar explosions with the
unique property that the light curves can be standardized, allowing them to be
used as distance indicators for cosmological studies. Many fundamental
questions bout these events remain, however. We provide a critique of our
present understanding of these and present results of simulations assuming the
single-degenerate progenitor model consisting of a white dwarf that has gained
mass from a stellar companion. We present results from full three-dimensional
simulations of convection with weak reactions comprising the A=23 Urca process
in the progenitor white dwarf.
