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

所提出的研究将提高无界域数值模拟的准确性和效率。研究流体动力学的两个重要领域。首先是基于完全匹配层（PML）技术的吸收边界条件的发展，用于湍流大涡模拟（LES）。在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PML技术在湍流大涡模拟中的进一步发展。提出了LES吸收方程的公式，以及其他湍流模拟，如随时间变化的Reynolds平均Navier-Stokes （RANS）模拟。第二个研究领域是气体动力学理论中玻尔兹曼- bgk方程数值格式的非反射边界条件的发展。建议的工作将基于完全匹配层方法开发，分析和实现吸收边界条件。本文还将对晶格玻尔兹曼法中PML吸收边界条件的实现和分析进行研究。由于无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，例如减少机身和喷气噪声，在反应流中的湍流燃烧研究中，以及在天气预报的数值模型中。在拟议的研究中开发的玻尔兹曼- bgk方程的PML适用于采用动力学理论的各种科学研究领域，例如多相和多组分流动，纳米技术中的微流体，微粒悬浮液和微机电系统（MEMS）中的微流动。

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).