A Model for Combustion in Strongly Stratified Environments

DMS奖摘要奖#：0202485PI：贝利斯，阿尔文研究所：西北大学项目：应用数学项目经理：凯瑟琳·马夫里普利斯题目：强层化环境中的燃烧模型我们开发并数值求解了恒星包层中的低马赫数爆燃模型。对于许多恒星环境，火焰或对流速度与声速的马赫数之比非常小(数量级为.01或更小)，因此对于基于全流体动力学的显式计算，时间步长受到声速的限制，因此需要过多的计算时间来模拟与爆燃和相关对流相关的相对较长的时间尺度。我们的模型过滤掉声波，同时考虑到强烈的垂直压力分层(数量级为十个数量级)。该模型的基础是通过在垂直坐标系中求解边值问题来预先计算强分层流体静力解。然后展开了关于该解的流体动力学方程。得到的速度和非静压系统然后按马赫数展开，有效地过滤掉声波，得到一个时间步长受流体和火焰速度而不是声速限制的系统。新模型将被应用于研究新星爆发期间吸积白矮星包层内的对流。该模型将允许在对流时间尺度上进行模拟，从而允许从理论上描述新星核燃烧的多维发展。我们建议在滤除声波的恒星包层中模拟核流体的流体动力学。这种环境的典型特征是，能量通过核反应释放，其方式类似于地面燃烧(核燃烧)。在许多这样的配置中，火焰速度和相关的流体速度比声速小得多。这限制了这些模型可以求解的时间长度，并有效地排除了与燃烧和对流相关的现象的模拟。例如，在中子星包层中燃烧的模拟需要大约30,000小时的净处理器时间，即并行的Silicon Graphics计算机上所有处理器的时间，大约200毫秒的模拟时间。对于这个问题，燃烧和对流的时间尺度大约是分钟，例如大约5分钟。因此，使用目前的模型对这种现象进行模拟和计算机分析是不可能的。我们预计，用拟议的新模型进行这种分析将是可行的，因为声学效应将被消除。该模型将用于研究白矮星新星的性质，特别是解决关于不同物种的混合在促进新星爆发中的作用的相互竞争的理论。该模型的数值解将使用并行算法和计算机，因此该项目将需要使用高性能计算来解释观测到的天体物理现象。日期：2002年6月21日

DMS Award AbstractAward #: 0202485PI: Bayliss, AlvinInstitution: Northwestern University Program: Applied MathematicsProgram Manager: Catherine MavriplisTitle: A Model for Combustion in Strongly Stratified EnvironmentsWe develop and solve numerically a low Mach number model for deflagrations in stellar envelopes. For many stellar environments the Mach number, the ratio of flame or convection speed to the sound speed, is very small (order .01 or less) so that for explicit computations based on full hydrodynamics timesteps are limited by the acoustic speeds, thus requiring excessive computation time to simulate the relatively long timescales associated with the deflagrations and associated convection flows. Our model filters out the sound waves while accounting for strong vertical pressure stratification (of the order of ten orders of magnitude). The model is based on initially pre-computing a strongly stratified hydrostatic solution by solving a boundary value problem in the vertical coordinate. The hydrodynamic equations are then expanded about this solution. The resulting system for the velocities and the non-hydrostatic pressure is then expanded in Mach number, effectively filtering out sound waves and yielding a system where timesteps are restricted by fluid and flame speeds rather than the sound speed. The new model will be applied to the study of convection in the envelope of an accreting white dwarf during a nova outburst. The model will allow simulation over convective timescales and thus allow a theoretical description of the multi-dimensional nuclear burning development of novae.We propose to simulate the hydrodynamics of nuclear fluids in a stellar envelope in which sound waves are filtered out. It is typical of such environments that energy is released via nuclear reactions in a manner similar to terrestrial combustion (nuclear combustion). In many such configurations the flame speed and associated fluid speeds are much smaller than the sound speed. This limits the length of time for which these models can be solved and effectively precludes a simulation of phenomena associated with the burning and convection. For example, a simulation of burning in a neutron star envelope required approximately 30,000 hours net processor time, i.e., the time for all processors on a parallel Silicon Graphics computer, for approximately 200 milliseconds of simulated time. For this problem, the burning and convection timescales were of the order of minutes, e.g., about 5 minutes. Thus, a simulation and computer analysis of such phenomena would be prohibitive using current models. We anticipate that such analyses would be feasible with the proposed new model, because acoustic effects would be eliminated. The model will be used to study the nature of white dwarf novae, and in particular to resolve competing theories regarding the role of mixing of different species in promoting nova outbursts. The numerical solution of the model will employ parallel algorithms and computers and thus the project will entail the use of high performance computing to explain observed astrophysical phenomena.Date: June 21, 2002