Adaptive low Mach number simulations of nuclear flame microphysics

We introduce a numerical model for the simulation of nuclear flames in Type Ia supernovae. This model is based on a low Mach number formulation that analytically removes acoustic wave propagation while retaining the compressibility effects resulting from nuclear burning. The formulation presented here generalizes low Mach number models used in combustion that are based on an ideal gas approximation to the arbitrary equations of state such as those describing the degenerate matter found in stellar material. The low Mach number formulation permits time steps that are controlled by the advective time scales resulting in a substantial improvement in computational efficiency compared to a compressible formulation. We briefly discuss the basic discretization methodology for the low Mach number equations and their implementation in an adaptive projection framework. We present validation computations in which the computational results from the low Mach number model are compared to a compressible code and present an application of the methodology to the Landau-Darrieus instability of a carbon flame. 1 The work of Bell, Day and Rendleman was supported by the Applied Mathematics Program of the DOE Office of Mathematics, Information, and Computational Sciences under the U.S. Department of Energy under contract No. DE-AC0376SF00098. 2 The work of Woosley and Zingale were supported by the Scientific Discovery through Advanced Computing (SciDAC) program of the DOE, grant number DEFC02-01ER41176 to the Supernova Science Center/UCSC. Preprint submitted to Elsevier Science 4 December 2003