Kinetic Theory Method for Large Eddy Simulation of Turbulence

9974289在这项工作中，我们计划探索和应用一种全新的方法来模拟湍流的大涡（LES），即使用玻尔兹曼动力学水平表示流动。传统的LES方法是基于在连续体水平上求解修正的Navier-Stokes方程组。虽然这种方法已经取得了许多有趣的结果，但它也遇到了内在的困难（例如，在边界处提供忠实的湍流行为）。由于晶格玻尔兹曼方法最近的成功，我们相信从一个新的角度来解决这个问题有很大的潜力。也就是说，我们建议使用玻尔兹曼方程来表示流体动力学。这种表示不仅适合于描述粒子运动，而且一旦建立适当的平均过程，也可能是研究大尺度流体湍流特性的一种有用方法。在这项工作中，我们计划通过制定这样的玻尔兹曼描述来开展一系列广泛的湍流动力学理论和计算研究。具体任务包括模型制定、仿真结果、记忆和历史效应、壁面模型和边界条件的重新制定以及多相湍流的初步应用。这里所做的工作可能会对我们在现实世界系统中模拟流体流动的能力产生持久的影响。湍流中涡旋尺寸的巨大范围使全尺寸系统的流动方程无法直接求解。晶格玻尔兹曼方法的新颖之处在于，它绕过了传统计算机的一些固有限制，以实现真实的流动模拟。通过将这种方法与大涡模拟的先进思想相结合，我们期望在这些困难的流动问题上取得否则不可能取得的进展。特别是，用于大涡模拟的晶格玻尔兹曼方法可以有效地表述迄今为止没有分析过的近壁边界条件。也有可能在这里建立的新公式将提出新的计算机架构，使全面的流动模拟成为可能。

9974289In this work, we plan to explore and apply a fundamentally new approach to large-eddy simulation (LES) of turbulence, viz. the use of a Boltzmann kinetic level representation of the flow. Conventional approaches to LES are based on solving a system of modified Navier-Stokes equations at the continuum level. While such an approach has achieved many interesting results, it also encounters intrinsic difficulties (e.g. in providing faithful turbulent behavior at boundaries). Owing to recent successes with the lattice Boltzmann method, we believe there is significant potential in approaching the problem from a new angle. That is, we propose the use of the Boltzmann equation representation of fluid dynamics. Such a representation is not only suitable for describing particle motions, but may also be a useful way of studying large-scale fluid turbulence properties once some appropriate averaging procedure is constructed. In this work, we plan to carry out an extensive series of theoretical and computational studies of turbulence dynamics by formulating such a Boltzmann description. The specific tasks include model formulation, simulation results, memory and history effects, reformulation of wall models and boundary conditions, and initial applications to multiphase turbulent flows.The work to be done here may have long-lasting impact on our ability to simulate fluid flows in real-world systems. The huge range of eddy sizes in turbulence precludes direct solution of the flow equations at all scales for full-scale systems. The novelty of the lattice Boltzmann method is that it circumvents some of the intrinsic limitations of conventional computers in order to achieve realistic flow simulations. By coupling of this method to advanced ideas on large-eddy simulation, we expect to achieve progress that would not otherwise be possible on these difficult flow problems. In particular, the lattice Boltzmann method for large-eddy simulation allows the efficient formulation of near-wall boundary conditions that have so far escaped analysis. It is also possible that the new formulations to be established here will suggest new computer architectures that will enable full-scale flow simulations.