发表机构
University of Colorado Denver（科罗拉多大学丹佛分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何用格子玻尔兹曼方法在一般正交坐标系中模拟纳维-斯托克斯方程，通过坐标变换适应非均匀聚类网格，构建新公式，保持方法简单性和伽利略不变性，经多种碰撞模型实现及验证，展现出计算优势。
AI 中文摘要
有效求解多尺度流体流动或边界层需要使用具有局部网格聚类的非均匀网格。然而，标准格子玻尔兹曼方法（LBM）限于均匀笛卡尔网格。本文提出新的改进LBM公式，通过坐标变换适应连续变化的空间网格，以在一般正交坐标系（GOC）中模拟纳维-斯托克斯方程（NSE）。利用查普曼-恩斯科格分析构建，使分布函数的平衡矩和碰撞步骤中的几何力项依赖于局部度量因子及其空间导数等。所得GOC-LBM保持了碰撞-流方法的简单性且伽利略不变，无三次速度伪影。它通用且模块化，可与任何碰撞模型配合使用。给出多种碰撞模型的实现细节，基于中心矩的多松弛时间模型最稳健。通过数值模拟验证了GOC-LBM，还展示了其在模拟边界层流动等案例中的显著计算优势。
英文摘要
Resolving multiscale fluid flows or boundary layers effectively requires the use of nonuniform meshes with local grid clustering. The standard lattice Boltzmann method (LBM), a kinetic theory-based approach for computational fluid dynamics, however, is restricted to the use of uniform Cartesian grids. We present new and improved formulations of the LBM that accommodate continuously varying spatial grids via coordinate transformations to simulate the Navier-Stokes equations (NSE) in the general orthogonal coordinates (GOC). They are constructed using a Chapman-Enskog analysis to specify the equilibrium moments of the distribution functions and the geometric force terms used in the collision step to be dependent on the local metric factors and their spatial derivatives, along with the density, momentum and their fluxes, and some correction terms related to the normal velocity gradients so as to accurately represent the NSE in the GOC. The resulting GOC-LBM importantly maintains the simplicity of the collide-and-stream approach and is Galilean invariant that is free of the cubic velocity artifacts. Our GOC-LBM is general and modular in that it can be used with any collision model with appropriate modifications to the equilibria and forcing terms. We present its implementation details for a variety of collision models while the central moments-based model using multiple relaxation times was found to be the most robust in practical implementations. We validate the GOC-LBM through numerical simulations for various benchmark flow problems. Moreover, we demonstrate significant computational advantages of our approach for a case study on simulating boundary layer flows efficiently that involves coupling the GOC-LBM for the NSE with a new GOC-LB scheme for solving the magnetic induction equation for magnetohydrodynamics (MHD), and for another case study involving orthogonal curvilinear grids.
Comments92 pages, 24 figures
