Low Mach number modeling of type Ia supernovae. III. Reactions

We continue the description of a low Mach number hydrodynamics algorithm for reacting, full star flows. Here we demonstrate how to accurately incorporate reactions using a second-order accurate Strang-splitting technique. We also improve the fidelity of the model by allowing the base state to evolve in response to large-scale convection as well as large-scale heating, taking care to account for the compositional changes to the base state as well. The new algorithm is tested via comparisons with a fully compressible code and shown to be in good agreement. The resulting code, MAESTRO, once extended to incorporate a spherically symmetric base state, will be used to study the convection and ignition phases of Type Ia supernovae.