cfd-12-05-计算网格技术_基础和结构化

Computational Fluid Dynamics计算流体力学（CFD）,第三讲：计算网格技术, 基础和结构化网格,Introduction,The numerical solution of partial differential equations requires some discretization of the field into a collection of points or elemental volumes (cells).,The differential equations are approximated by a set of algebraic equations on this collection, which can be solved to produce a set of discrete values that approximate the solution of the PDE over the field.,Grid generation is the process of determining the coordinate transformation that maps the body-fitted non-uniform non- orthogonal physical space x,y,z,t into the transformed uniform orthogonal computational space ,.,Choice of grid,结构化网格,直角网格,三角形网格,Choice of grid,Simple/regular geometries (e.g. pipe, circular cylinder)： The grid lines usually follow the coordinate directions.,Complex geometries (Boundary-Fitted Non-Orthogonal Grids)： Grid Types: (1). Structured (2). Block-structured (3). Unstructured,Complex geometries (Boundary-Fitted Non-Orthogonal Grids)： Advantages: (1). Can be adapted to any geometry (2). Boundary conditions are easy to apply (3). Grid spacing can be made smaller in regions of strong variable variation.,Disadvantages: (1). The transformed equations contain more terms thereby increasing both the difficulty of programming and the cost of solving the equations (2). The grid non-orthogonality may cause unphysical solutions.,Complex geometries (Boundary-Fitted Non-Orthogonal Grids)：,structured,Block-structured with matching interface,Unstructured,Block-structured without matching interface,早期有限差分方法应用于实际问题时物面边界的近似处理方法,Choice of grid,如果求解区域不规则，当用等步长网格把物理区域离散 后，除了与边界相邻的网格点以外，各个内点可以很简 单构造二阶或高阶格式，而在与边界相邻的网格点上则 很难保持格式精度,计算时数据管理变得较为复杂,边界条件往往需要通过内插或外插来起作用，由于网格 线与边界不垂直，不便于 这类边界条件的使用，会带 来较大误差,网格发展思路之一： 贴体结构化网格,网格发展思路之二： 贴体非结构化网格,网格发展思路之三： 直角网格,Grid generation,结构化网格生成方法（structured grid） 三角形网格生成方法（triangle/tetrahedron） 直角网格生成方法（Cartesian grid）,（structured grid generation method）,结构化网格的生成方法大致分为代数方法、保角变换方法和求解偏微分方程方法三类，其各具优缺点和适用范围。,生成贴体及与边界正交的具有多块结构的高质量网格，实现对网格的物面正交性、法向光顺性及周向均匀性的多重控制。,结构化网格生成方法,Conformal mapping: Based on complex variable theory, which is limited to two dimensions.,Algebraic methods: 1. 1D: Polynomials, Trigonometric functions, Logarithmic functions. 2. 2D: Orthogonal one-dimensional transformation, normalizing transformation, connection functions 3. 3D: Stacked two-dimensional transformations, superelliptical boundaries.,Differential equation methods: Step 1: Determine the grid point distribution on the boundaries of the physical space. Step 2: Assume the interior grid point is specified by a differential equation that satisfies the grid point distributions specified on the boundaries and yields an acceptable interior grid point distribution.,Commercial software (Gridgen, Gambit, etc.),Examples,(a) Symmetric (b) centerbody (c) asymmetric,求解偏微分方程方法：,椭圆型偏微分方程,Hilgenstock 源项修正方法,求解偏微分方程方法：,法向外推方法中的推进方向计算：( Stretched grids ),结构化网格,单块网格,多块网格,网格拓扑结构：,Grid topology,Grid topology,Topology of “O” type grid,Topology of “C” type grid,Topology of “H” type grid,按照网格生成权威 Joe F. Thompson 的意见（AGARD CP-464，1989） 将 “ block ” 、“ patched ”、“ zonal ” 等网格统一称作 “ multi-block ”，即多块网格将 “ chimera ”、“ embedded ”、“ overlaid ”、“ overlapped ” 等网格统一称作 “ chimera ”，即嵌套网格,multi-block 、多块网格,chimera 、嵌套网格,分块策略： 第一种：要求块与块之间的交界面是一个完整的 网格边界面 第二种：允许块与块之间的交界面是部分搭接的 关系,1,2,3,4,5,1,1,2,2,3,3,4,5,4,5,多块分区示意图,Complex geometries (Chimera grid)： 1. Definition: Use of a set of grids to cover irregular solution domains.,2. Advantages: (1). Reduce substantially the time and efforts to generate a grid, especially for 3D configurations with increasing geometric complexity. (2). It allows without additional difficulty calculation of flows around moving bodies.,3. Disadvantages: (1). The programming and coupling of the grids can be complicated. (2). Difficult to maintain conservation at the interfaces. (3). Interpolation process may introduce errors or