Low mach number modeling of type Ia supernovae. II. Energy evolution

The convective period leading up to a Type Ia supernova (SN Ia) explosion is characterized by very low Mach number flows, requiring hydrodynamic methods well-suited to long-time integration. We continue the development of the low Mach number equation set for stellar-scale flows by incorporating the effects of heat release due to external sources. Low Mach number hydrodynamics equations with a time-dependent background state are derived, and a numerical method based on the approximate projection formalism is presented. We demonstrate through validation with a fully compressible hydrodynamics code that this low Mach number model accurately captures the expansion of the stellar atmosphere as well as the local dynamics due to external heat sources. This algorithm provides the basis for an efficient simulation tool for studying the ignition of SNe Ia.