南方科技大学知识苑(SUSTech KC): 可压缩高阶格子玻尔兹曼算法研究—

题名	可压缩高阶格子玻尔兹曼算法研究——体力项建模及流体固壁边界条件
其他题名	HIGH ORDER LATTICE BOLTZMANN METHOD FOR COMPRESSIBLE FLOW: BODY FORCE MODELLING AND BOUNDARY CONDITION
姓名	李作旭
姓名拼音	LI Zuoxu
学号	12032387
学位类型	硕士
学位专业	080103 流体力学
学科门类/专业学位类别	08 工学
导师	单肖文
导师单位	力学与航空航天工程系
论文答辩日期	2023-05-10
论文提交日期	2023-06-30
学位授予单位	南方科技大学
学位授予地点	深圳
摘要	准确模拟可压缩流动对指导生产实践有着重要意义，如新型飞机的气动设计、天气的准确预测、内燃机和制冷机的设计等等。格子玻尔兹曼方法 (Lattice Boltzmann Method LBM) 作为高效的计算流体力学方法之一，最初被用以模拟近不可压缩流动。近年来，LBM 被重新公式化为 Boltzmann BGK 方程的速度空间离散，能够恢复完整的理想气体的 Navier Stokes Fourier (NSF) 方程，以应对各种现实工程领域的挑战。但是，尚有一些问题仍需深入讨论，如体力项的高阶矩对能量方程的作用；高阶 LBM 算法的边界条件等等。基于现在可压缩高阶 LBM 算法研究的不足，本文重点深入研究了高阶 LBM 的体力格式及其边界条件。现将本文研究内容总结如下：提出一种通用的，系统性的在 LBM 中结合体积力的方法，可以有效的模拟热可压缩流动及非平衡流动。新格式的创新和关键之处在于加入了体力项的第三阶矩。通过 Chapman-Enskog 展开分析发现，体力项的三阶矩的缺省将在恢复的宏观热流中产生非物理的误差项。新的误差项为马赫数的三次方量级，温差的一次方量级，并且在可压缩流动中不可忽略。这些理论发现以及体力项的三阶矩的必要性通过数值算例得到验证。提出了适用于多速 LBM，适用于模拟复杂几何下的热可压缩流动的，严格满足质量守恒的 LBM 边界条件。我们将基于体积分数的曲型边界条件 [Chen et al, Int. J. Mod. Phys, C, 9, 1281, (1998)] 拓展到多速度 LBM。提出了密度分布函数及内部自由度能量分布函数的边界条件。一系列数值实验，包括平直/倾斜的可压缩Couette 流动、可压缩 Taylor Couette 层流、可压缩 Rayleigh-Bénard 流动和同心圆环内的自然对流，证明了当前边界条件具有严格的质量守恒和接近二阶的数值精度。提出了热对流系统中新的无量纲参数相对密度比 Dr，用以描述重力场和温度梯度对密度的影响之比。理论分析和数值实验均表明：当 Dr 偏离 0 时，即使在小温差假设下，Boussinesq 近似不再成立。
其他摘要	Accurate simulation of compressible flow is of great significance to guide human production practices, such as the aerodynamic design of new aircraft, accurate weather prediction, and the design of internal combustion engines and refrigerators. Lattice Boltz mann Method (LBM), as one of the most efffficient computational fluid dynamics methods, was initially applied to mimic the motion of a near-incompressible fluid. In recent years the method was re-formulated as a velocity-space discretization of the Boltzmann-BGK equation capable of recovering the full Navier-Stokes-Fourier (NSF) equations to answer the challenges in various real-life engineering fields. However, there are still some issues to be discussed in depth, such as effect of the high order moments of the body force term on the energy equation, boundary condition of high order LBM and so on. Based on the shortages of the current research on compressible higher-order LBM algorithm, this thesis focuses on the in-depth study of the forcing scheme and boundary condition of high order LBM. The research contents of this thesis are summarized as follows. We present a systematic approach of incorporating body force in LBM which is valid for thermal compressible and non-equilibrium flows. In particular, a LBM forcing scheme accurate for the energy equation with second-order time accuracy is given. New and essential in this scheme is the third-moment contribution of the force term. It is shown via Chapman-Enskog analysis that the absence of this contribution causes an erroneous heat flux quadratic in Mach number and linear in temperature variation. The theoretical findings are verified and the necessity of the third-moment contribution demonstrated by numerical simulations. We extend the volumetric boundary condition for curved boundaries [Chen et al, Int. J. Mod. Phys, C, 9, 1281, (1998)] to multi-speed lattice Boltzmann models for thermal compressible flows. We propose the boundary conditions of density distribution function and distribution function of internal freedom energy. Several numerical tests, including flat/inclined compressible Couette flow, compressible laminar Taylor-Couette flow, compressible Rayleigh-Bénard convection and natural convection in a concentric annulus, confirm that the boundary condition has exact mass conservation and an accuracy close to second order. For thermal convection, the density variation ratio 𝐷𝑟 is defined to depict influence of gravity on density, compared with temperature difference. The theoretical analysis and numerical tests indicate the Boussinesq assumption isn’t valid when 𝐷𝑟 deviates from zero even for small temperature variation.
关键词	格子玻尔兹曼算法可压缩流动体积力格式边界条件
其他关键词	Lattice Boltzmann Compressible Forcing Scheme Boundary Condition
语种	中文
培养类别	独立培养
入学年份	2020
学位授予年份	2023-05
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所在学位评定分委会	力学
国内图书分类号	中国
来源库	人工提交
成果类型	学位论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/544674
专题	工学院_力学与航空航天工程系
推荐引用方式 GB/T 7714	李作旭. 可压缩高阶格子玻尔兹曼算法研究——体力项建模及流体固壁边界条件[D]. 深圳. 南方科技大学,2023.

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