A Model for Combustion in Strongly Stratified Environments

获奖摘要获奖编号：0202485PI: Bayliss， AlvinInstitution: Northwestern University项目：应用数学项目经理：Catherine mavriplis标题：强分层环境中的燃烧模型我们开发并数值求解了恒星包层中燃烧的低马赫数模型。对于许多恒星环境，马赫数，即火焰或对流速度与声速之比，是非常小的。01或更小)，因此，对于基于全流体力学的显式计算，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流动相关的相对较长的时间尺度。我们的模型过滤掉了声波，同时考虑到强大的垂直压力分层（10个数量级）。该模型是基于通过求解垂直坐标上的边值问题，初步预计算一个强分层流体静力解。然后围绕这个解展开流体动力学方程。由此得到的速度和非静水压力系统在马赫数上进行了扩展，有效地过滤掉了声波，并产生了一个时间步长受流体和火焰速度而不是声速限制的系统。新模型将应用于新星爆发期间吸积白矮星包络层内对流的研究。该模型将允许在对流时间尺度上进行模拟，从而允许对新星的多维核燃烧发展进行理论描述。我们建议在声波被过滤掉的恒星包层中模拟核流体的流体动力学。在这种环境中，能量通过核反应以类似于陆地燃烧（核燃烧）的方式释放是典型的。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有关的现象的模拟。例如，在中子星外壳中燃烧的模拟需要大约30,000小时的净处理器时间，即在并行硅图形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为分钟数量级，例如约为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，这种分析是可行的，与提出的新模型，因为声学影响将被消除。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混合在促进新星爆发中的作用的竞争理论。该模型的数值解将采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