A Model for Combustion in Strongly Stratified Environments

强分层环境中的燃烧模型

• 批准号: 0202485
• 负责人: Alvin Bayliss
• 金额: --
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0202485&HistoricalAwards=false
• 关键词: Model; Combustion; Strongly; Stratified; Environments

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

DMS奖Abstractaward＃：0202485PI：AlvinInstitution：Northwestern University计划：应用数学课程经理：Catherine Mavriplistitle：catherine Mavriplistitle：在强烈分层环境中燃烧的模型开发和在数值上溶解了Stellarrar Enlelvelops中偏移的较低的Mach数模型。对于许多恒星环境，马赫数，火焰或对流速度与声速的比率非常小（订单.01或更少），因此，对于基于完整流体动力学的明确计算，基于完整的流体动力学时间段的明确计算受声速的限制，因此需要过度的计算时间来模拟与避免相关的对流和相关的对流和相关的对流式和相关的对流和相关的对流。 我们的模型在考虑强垂直压力分层的同时（十个数量级的订单）过滤了声波。 该模型基于最初通过在垂直坐标中解决边界值问题来预先计算强大的静水溶液。然后将流体动力方程扩展到该解决方案上。然后将最终的速度系统和非静态压力的系统扩展到马赫数中，有效地过滤声波，并产生一个系统，在该系统中，该系统受到时间段的流体和火焰速度限制，而不是声速。 新模型将应用于在Nova爆发期间积聚白矮人的信封中的对流研究。 该模型将允许对流时间尺度进行模拟，从而允许对Novae的多维核燃烧发展进行理论描述。我们建议在恒星信封中模拟核流体的流体动力学，其中声波被过滤掉。 这种环境的典型是，能量是通过类似于陆生燃烧（核燃烧）的方式来通过核反应释放的。在许多这样的配置中，火焰速度和相关的流体速度比音速小得多。这限制了可以解决这些模型的时间长度，并有效地排除了与燃烧和对流相关的现象的模拟。 例如，对中子恒星包膜中燃烧的模拟需要大约30,000小时的净处理器时间，即，在平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几分钟的顺序，例如，大约5分钟。 因此，使用当前模型对这种现象进行模拟和计算机分析将是令人望而却步的。我们预计该分析对于拟议的新模型将是可行的，因为将消除声学效应。 该模型将用于研究白色矮人Novae的性质，尤其是解决有关不同物种在促进Nova爆发中混合的作用的竞争理论。 该模型的数值解决方案将采用平行算法和计算机，因此该项目将需要使用高性能计算来解释观察到的天体物理现象。日期：2002年6月21日