Two Dimensional Simulations of Pair-Instability Supernovae

We present preliminary results from two dimensional numerical studies of pair instability supernova (PSN). We study nuclear burning, hydrodynamic instabilities and explosion of very massive stars. Use a new radiation-hydrodynamics code, CASTRO.Comment: Proceedings of "The First Stars and Galaxies: Challenges for the Next Decade", Austin, Texas, March 8-11, 2010. 2 pages, 1 figur

A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations

We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using appropriate invariant variables such that terms resulting from phase change are eliminated in the governing equations. In the second approach, which is a two-step scheme, separate transport equations for liquid water and vapor water are used, and no conversion between water vapor and liquid water is allowed in the first step, while in the second step a saturation adjustment procedure is performed that correctly allocates the water into its two phases based on the Clausius-Clapeyron formula. The numerical techniques we describe are first validated by comparing to a well-established benchmark problem. Particular attention is then paid to the effect of changing the time scale at which the moist variables are adjusted to the saturation requirements in two different variations of the two-step scheme. This study is motivated by the fact that when acoustic modes are integrated separately in time (neglecting phase change related phenomena), or when sound-proof equations are integrated, the time scale for imposing saturation adjustment is typically much larger than the numerical one related to the acoustics

Multi-Dimensional Simulations of Pair-Instability Supernovae

We present preliminary results from multidimensional numerical studies of pair instability supernova (PSN), studying the fluid instabilities that occur in multiple spatial dimensions. We use the new radiation-hydrodynamics code, CASTRO, and introduce a new mapping procedure that defines the initial conditions for the multidimensional runs in such a way that conservation of physical quantities is guaranteed at any level of resolution.Comment: Accepted for publication in Computer Physics Communications. 3 pages. 2 fig

White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.Comment: Accepted for publication in the Astrophysical Journa

Conservative Initial Mapping For Multidimensional Simulations of Stellar Explosions

Mapping one-dimensional stellar profiles onto multidimensional grids as initial conditions for hydrodynamics calculations can lead to numerical artifacts, one of the most severe of which is the violation of conservation laws for physical quantities such as energy and mass. Here we introduce a numerical scheme for mapping one-dimensional spherically-symmetric data onto multidimensional meshes so that these physical quantities are conserved. We validate our scheme by porting a realistic 1D Lagrangian stellar profile to the new multidimensional Eulerian hydro code CASTRO. Our results show that all important features in the profiles are reproduced on the new grid and that conservation laws are enforced at all resolutions after mapping.Comment: 7 pages, 5 figures, Proceeding for Conference on Computational Physics (CCP 2011

Simulation of lean premixed turbulent combustion

There is considerable technological interest in developingnew fuel-flexible combustion systems that can burn fuels such ashydrogenor syngas. Lean premixed systems have the potential to burn thesetypes of fuels with high efficiency and low NOx emissions due to reducedburnt gas temperatures. Although traditional scientific approaches basedon theory and laboratory experiment have played essential roles indeveloping our current understanding of premixed combustion, they areunable to meet the challenges of designing fuel-flexible lean premixedcombustion devices. Computation, with itsability to deal with complexityand its unlimited access to data, hasthe potential for addressing thesechallenges. Realizing this potential requires the ability to perform highfidelity simulations of turbulent lean premixed flames under realisticconditions. In this paper, we examine the specialized mathematicalstructure of these combustion problems and discuss simulation approachesthat exploit this structure. Using these ideas we can dramatically reducecomputational cost, making it possible to perform high-fidelitysimulations of realistic flames. We illustrate this methodology byconsidering ultra-lean hydrogen flames and discuss how this type ofsimulation is changing the way researchers study combustion