Low mach number modeling of convection in helium shells on sub-chandrasekhar white dwarfs. I. methodology

We assess the robustness of a low Mach number hydrodynamics algorithm for modeling helium shell convection on the surface of a white dwarf in the context of the sub-Chandrasekhar model for Type Ia supernovae. We use the low Mach number stellar hydrodynamics code, MAESTRO, to perform three-dimensional, spatially adaptive simulations of convection leading up to the point of the ignition of a burning front. We show that the low Mach number hydrodynamics model provides a robust description of the system.