The explosion of a Type Ia supernova (SNIa) begins as a turbulent flame deep within a 1.4 solar-mass white dwarf. Initially the burning happens in the flamelet regime where turbulence only serves to wrinkle and fold an essentially laminar burning front. However, as the star expands and the flame moves outwards, it encounters regions of lower density. At ∼ 2 × 10g cm, the flame transitions to a ...

The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniform...

We develop a low Mach number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure that generalizes our prior work on ideal mixtures of ideal gases [K. In this formulation we combine and extend a number of existing descriptions of multispecies transport available in t...

Two semi-implicit methods based on the splitting of the Euler equations ux into uid and acoustic parts applied to low Mach number ows are presented. The rst method is based on the splitting of slow and fast eigenvalues of the jacobian matrix of the uxes and a semi-implicit scheme is constructed by introducing only the fast eigenvalues in the implicit matrices. The second method is based on the ...

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant...

Aleksandar Donev, ∗ Andy Nonaka, Yifei Sun, 3 Thomas G. Fai, Alejandro L. Garcia, and John B. Bell Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 Center for Computational Science and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 Leon H. Charney Division of Cardiology, Department of Medicine, New York University School of Medicine, N...

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We continue the description of a lowMach 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 ...

A robust AUSM upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of ...