A Model for Combustion in Strongly Stratified Environments

DMS Award AbstractAward #： 0202485 PI： Bayliss，Alvin机构： 西北大学课程： 应用数学项目经理：Catherine Mavriplis职务：强分层环境中的燃烧模型建立了一个低马赫数的恒星包层爆燃模型，并进行了数值求解。对于许多恒星环境的马赫数，火焰或对流速度与声速的比率，是非常小的（0.01或更小），使得对于基于全流体动力学时间步长的显式计算，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联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（十个数量级）。 该模型是基于最初预先计算一个强分层的流体静力学解决方案，通过解决边界值问题的垂直坐标。然后将流体动力学方程组关于此解展开。然后将所得的速度和非流体静压系统扩展到马赫数，有效地过滤掉声波并产生一个系统，其中时间步长受流体和火焰速度而不是声速的限制。 新模型将用于研究新星爆发期间吸积白色矮星包层中的对流。 该模型将允许模拟对流的时间尺度，从而允许理论描述的多维核燃烧的发展novae.We建议模拟核流体的流体动力学在一个恒星的信封中，声波被过滤掉。 这种环境的典型特征是，能量通过核反应以类似于地球燃烧（核燃烧）的方式释放。在许多这样的配置中，火焰速度和相关联的流体速度比声速小得多。这就限制了求解这些模型的时间长度，并有效地排除了与燃烧和对流有关的现象的模拟。 例如，模拟中子星星包层中的燃烧需要大约30，000小时的净处理器时间，即，并行Silicon Graphics计算机上所有处理器的时间，大约为200毫秒的模拟时间。 对于这个问题，燃烧和对流的时间尺度是分钟的量级，例如，大约五分钟。 因此，使用当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，这种分析将是可行的，与拟议的新模型，因为声学效应将被消除。 该模型将用于研究白色矮新星的性质，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。

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