Analysis and implementation of accurate numerical boundary conditions for Large Eddy Simulations and Boltzmann equation

拟议的研究将提高无界域数值模拟的准确性和效率。对流体动力学的两个重要领域进行了研究。第一个是基于完美匹配层 (PML) 技术的湍流大涡模拟 (LES) 吸收边界条件的开发。继最近成功地将完美匹配层方法扩展到非线性欧拉和纳维-斯托克斯方程之后，提出了进一步开发用于湍流大涡模拟的 PML 技术。提出了 LES 吸收方程的公式以及其他湍流模拟，例如瞬态雷诺平均纳维斯托克斯 (RANS) 模拟。第二个研究领域是气体动力学理论中 Boltzmann-BGK 方程数值格式的非反射边界条件的开发。拟议的工作将基于完美匹配层方法开发、分析和实施吸收边界条件。格子玻尔兹曼方法中 PML 吸收边界条件的实现和分析也将在拟议的研究中进行。由于非反射边界的普遍存在以及大涡模拟在复杂湍流计算研究中的重要性，拟议的工作将对计算流体动力学和计算声学中广泛的数值模拟的质量和效率产生直接影响，例如在机身和喷气噪声的减少中，在反应流中的湍流燃烧研究中，以及天气预报的数值模型。所提出的研究中开发的 Boltzmann-BGK 方程的 PML 适用于采用动力学理论的科学研究的各个领域，例如多相流和多组分流、纳米技术中的微流体、微机电系统 (MEMS) 中的颗粒悬浮液和微流。

Proposed research will improve the accuracy and efficiency of numerical simulations in unbounded domains. Investigations in two important areas of fluid dynamics are pursued. The first is the development of absorbing boundary conditions based on the Perfectly Matched Layer (PML) technique for Large Eddy Simulation (LES) of turbulent flows. Following recent successes of extending the Perfectly Matched Layer methodology to the nonlinear Euler and Navier-Stokes equations, further development of the PML technique for Large Eddy Simulation of turbulent flows is proposed. Formulations of absorbing equations for LES, as well as other turbulent flow simulation, such as the time-dependent Reynolds Averaged Navier-Stokes (RANS) simulations, are proposed. The second area of research is the development of non-reflecting boundary conditions for numerical schemes for the Boltzmann-BGK equation in gas kinetic theory. Proposed work will develop, analyze and implement the absorbing boundary condition based on the Perfectly Matched Layer methodology. Implementation and analysis of PML absorbing boundary condition in the Lattice Boltzmann Method will also be carried out in proposed research.Due to the ubiquity of non-reflecting boundaries and the importance of Large Eddy Simulation in the computational studies of complex turbulent flows, proposed work will have a direct impact on the quality and efficiency of a broad class of numerical simulations in computational fluid dynamics and computational acoustics, such as in the reduction of airframe and jet noises, in studies of turbulent combustion in reactive flows, and in numerical models for weather predictions. The PML for the Boltzmann-BGK equation developed in proposed research is applicable to a diverse field of scientific investigations that employ the kinetic theory, such as multiphase and multi-component flows, microfluidics in nanotechnologies, particle suspensions and microflows in micro-electro-mechanical systems (MEMS).