  We introduce a low Mach number equation set for the large-scale numerical
simulation of carbon-oxygen white dwarfs experiencing a thermonuclear
deflagration. Since most of the interesting physics in a Type Ia supernova
transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a
considerable increase in accuracy and savings in computer time compared with
frequently used compressible codes. Our equation set is derived from the fully
compressible equations using low Mach number asymptotics, but without any
restriction on the size of perturbations in density or temperature. Comparisons
with simulations that use the fully compressible equations validate the low
Mach number model in regimes where both are applicable. Comparisons to
simulations based on the more traditional anelastic approximation also
demonstrate the agreement of these models in the regime for which the anelastic
approximation is valid. For low Mach number flows with potentially finite
amplitude variations in density and temperature, the low Mach number model
overcomes the limitations of each of the more traditional models and can serve
as the basis for an accurate and efficient simulation tool.
