基于同位网格下求解N-S方程的快速算法

在有限容积法基础上建立了基于同位网格的SIMPLEM算法。此算法使初始压力场与速度场耦合,让压力场和速度场同时更好地满足动量方程和连续性方程,且兼顾考虑扩散对流项对计算节点速度修正值的影响及源项与速度场之间的同步性,详细给出了算法的推导过程且对方腔顶盖驱动流进行了数值模拟。计算节点的布置采用同位网格技术,界面流速通过动量插值确定,在不同条件下讨论了迭代次数与残差的关系和不同算法的收敛性,同时验证了算法及程序是准确和可信的。     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

基于建筑风场数值模拟的网格层块加密法

在建筑风场的数值模拟中,当前普遍采用的离散网格多是计算前一次性布置的固定网格,通常很难适应实际流场变量的变化要求.为提高数值模拟的精度,基于结构化同位网格系统及控制容积离散微分方程的方法,将适应性网格局部加密(AMR)的思想引入到采用压力校正迭代算法的建筑风场模拟中,提出了一种半自适应的层块网格加密方法.该方法可结合误差分析对误差较大的区域网格实行自动判别并实施逐层块状加密.算例分析表明,该方法能在较高的效益下提高数值解的精度.     

一类面向高阶精度自适应流动计算的流场插值方法

网格自适应技术和高阶精度数值方法是提升计算流体力学复杂问题适应能力的有效技术途径. 将这两项技术结合需要解决一系列技术难题, 其中之一是高阶精度流场插值. 针对高阶精度自适应流动计算, 提出一类高精度流场插值方法, 实现将前一迭代步网格中流场数值解插值到当前迭代步网格中, 以延续前一迭代步中的计算状态. 为实现流场插值过程中物理量守恒, 该方法先计算新旧网格的重叠区域, 然后将物理量从重叠区域的旧网格中转移到新网格中. 为满足高阶精度要求, 先采用k-exact最小二乘方法对旧网格上的数值解进行重构, 获得描述物理量分布的高阶多项式, 随后采用高阶精度高斯数值积分实现物理量精确地转移到新网格单元上. 最后, 通过一个具有精确解的数值算例和一个高阶精度自适应流动计算算例验证了本文算法的有效性. 第一个算例结果表明当网格规模固定不变时, 插值精度阶数越高, 插值误差越小; 第二个算例显示本文方法可以有效缩短高精度自适应流动计算的迭代收敛时间.      

拼接网格技术在复杂流场数值模拟中的应用研究

采用分区拼接网格技术,对 DLR-F6 机翼/机身胜架/短舱复杂组合体进行拼接网格分布.并采用 Menter SST 湍流模型,通过求解 Navier-Stokes 方程,对该组合体外流场以及发动机短舱内流场进行了一体化数值模拟,与相应风洞实验数据及分区搭接网格计算结果进行了比较与分析,验证了拼接网格技术的高效性与可靠性.同时通过分析对比不同插值方法的计算结果,研究了插值方法对拼接精度的影响;通过分析对比几组不同的拼接网格算例,总结出了 3 个拼接网格的基本实施准则.证明了拼接网格能够大幅度减小计算网格数目,可以更加灵活地分布网格节点,这样既可以缩短计算时间,又可以降低对内存的需求,提高了计算效率;同时无论整体的力系数,还是局部的压力分布流场细节都能够满足工程精度.     

基于分区拼接网格技术高升力装置流场数值模拟

针对高升力装置构型模型结构复杂、流场变化剧烈等特点,本文采用分区拼接网格的思想分别按照流场和结构拓扑特点对高升力装置进行了网格分区。在分区的基础上逐块生成网格,减小了增升装置网格的生成难度,提高了网格质量,减少了网格数目。首先,研究了高升力装置的分区策略及流场特点;接着以MD30P-30N多段翼型为研究算例研究了网格比例和插值方法对计算结果的影响。经过分析对比可知:外部区域与近壁区域之间的比例不宜小于1:5;内部域网格比例不宜超过1:1.8,最好保持在1:1左右;计算中应该采用高阶精度插值以保证计算精度。采用某四段翼型进行了验证;最后采用NASA标准高升力装置进行了三维高升力装置流场数值模拟并与相应风洞实验数据及对接网格计算结果进行了比较与分析,验证了拼接网格技术的高效性与可靠性。同时分析研究了绕三维增升装置的流动及其周围复杂的粘性流动现象。     

一种基于增量径向基函数插值的流场重构方法

由于流场参数重构中, 用于重构的基网格单元的物理参数波动量相对于均值较小, 径向基函数（RBF） 直接插值方法重构会产生较大的数值振荡, 论文提出了一种增量RBF 插值方法, 并用于有限体积的流场重构步, 明显改善了插值格式的收敛性和稳定性. 算例首先通过简单的一维模型说明该方法的有效性, 当目标函数波动量相对于均值为小量时, 增量RBF 插值能够抑制数值振荡; 进一步通过二维亚音速、跨音速定常无黏算例、静止圆柱绕流非定常算例以及超音速前台阶算例来说明该方法在典型流场数值求解中的通用性和有效性. 研究表明增量RBF 重构方法可陡峭地捕捉激波间断, 可有效改善流场求解的收敛性和稳定性, 数值耗散小, 计算效率高.      

A RECONSTRUCTION METHOD FOR FINITE VOLUME FLOW FIELD SOLVING BASED ON INCREMENTAL RADIAL BASIS FUNCTIONS

由于流场参数重构中, 用于重构的基网格单元的物理参数波动量相对于均值较小, 径向基函数（RBF） 直接插值方法重构会产生较大的数值振荡, 论文提出了一种增量RBF 插值方法, 并用于有限体积的流场重构步, 明显改善了插值格式的收敛性和稳定性. 算例首先通过简单的一维模型说明该方法的有效性, 当目标函数波动量相对于均值为小量时, 增量RBF 插值能够抑制数值振荡; 进一步通过二维亚音速、跨音速定常无黏算例、静止圆柱绕流非定常算例以及超音速前台阶算例来说明该方法在典型流场数值求解中的通用性和有效性. 研究表明增量RBF 重构方法可陡峭地捕捉激波间断, 可有效改善流场求解的收敛性和稳定性, 数值耗散小, 计算效率高.     

基于Fluent平衡大气边界层流场模拟及应用

采用Fluent进行平衡大气边界层流场模拟,在地面边界引入气动粗糙壁面函数,上边界分别采用剪力驱动和速度驱动。首先对平坦区域进行流场模拟,然后基于模拟的流场对立方体建筑物表面风压分布进行了计算。结果表明:基于本文的边界条件设置方法,三种k-ε湍流模型均能获得良好的自保持性平衡大气边界层流场;在地面边界引入气动粗糙壁面函数,可实现任意类型的平衡大气边界层流场模拟,且对近地单元的高度无限制,有利于精细化网格计算;在上边界采用剪力驱动和速度驱动是等效的,采用速度驱动边界条件有利于提高计算效率;三种k-ε湍流模型计算的立方体中心面表面压力分布基本在测量值变化范围内,说明基于本文的平衡大气边界层流场可应用于结构风荷载数值模拟研究中。     

FV/MC混合算法求解轴对称钝体后湍流流场

介绍一种有限容积／Monte Carlo结合求解湍流流场的相容的混合算法．有限容积法求解Reynolds平均的动量方程和能量方程，Monte Carlo方法求解模化的脉动速度—频率—标量联合的PDF方程．将该算法发展到无结构网格，探讨了在无结构网格中实现两种方法的耦合，包括颗粒定位，颗粒场和平均场之间数据交换等问题．并以二维轴对称钝体后湍流流场作为算例，比较了计算结果与实验结果．     

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.     

非正交同位网格下压力与速度耦合算法

发展了一种在非正交同位网格下以笛卡儿速度分量作为动量方程的独立变量、压力与速度耦合的S IM-PLER算法。该算法的特点是显式处理界面速度中的压力交叉导数项,得出压力与压力修正方程,使得压力及压力修正值与界面逆变速度直接耦合。通过对分汊通道内的流动问题进行验证计算,结果表明该算法可以有效而准确地模拟复杂区域内的流动与换热问题。     

An immersed boundary finite difference method for LES of flow around bluff shapes

A three‐dimensional numerical model using large eddy simulation (LES) technique and incorporating the immersed boundary (IMB) concept has been developed to compute flow around bluff shapes. A fractional step finite differences method with rectilinear non‐uniform collocated grid is employed to solve the governing equations. Bluff shapes are treated in the IMB method by introducing artificial force terms into the momentum equations. Second‐order accurate interpolation schemes for all sorts of grid points adjacent to the immersed boundary have been developed to determine the velocities and pressure at these points. To enforce continuity, the methods of imposition of pressure boundary condition and addition of mass source/sink terms are tested. It has been found that imposing suitable pressure boundary condition (zero normal gradient) can effectively reproduce the correct pressure distribution and enforce mass conservation around a bluff shape. The present model has been verified and applied to simulate flow around bluff shapes: (1) a square cylinder and (2) the Tsing Ma suspension bridge deck section model. Complex flow phenomena such as flow separation and vortex shedding are reproduced and the drag coefficient, lift coefficient, and pressure coefficient are calculated and analyzed. Good agreement between the numerical results and the experimental data are obtained. The model is proven to be an efficient tool for flow simulation around bluff bodies in time varying flows. Copyright © 2004 John Wiley & Sons, Ltd.     

A conservative unstructured scheme for rapidly varied flows

This article introduces a new semi‐implicit, staggered finite volume scheme on unstructured meshes for the modelling of rapidly varied shallow water flows. Rapidly varied flows occur in the inundation of dry land during flooding situations. They typically involve bores and hydraulic jumps after obstacles such as road banks. Near such sudden flow transitions, the grid resolution is often low compared with the gradients of the bathymetry. Locally the hydrostatic pressure assumption may become invalid. In these situations, it is crucial to apply the correct conservation properties to obtain accurate results. An important feature of this scheme is therefore its ability to conserve momentum locally or, by choice, preserve constant energy head along a streamline. This is achieved using a special interpolation method and control volumes for momentum. The efficiency of inundation calculations with locally very high velocities, and in the case of unstructured meshes locally very small grid distances, is severely hampered by the Courant condition. This article provides a solution in the form of a locally implicit time integration for the advective terms that allows for an explicit calculation in most of the domain, while maintaining unconditional stability by implicit calculations only where necessary. The complex geometry of flooded urban areas asks for the flexibility of unstructured meshes. The efficient calculation of the pressure gradient in this, and other semi‐implicit staggered schemes, requires, however, an orthogonality condition to be put on the grid. In this article a simple method is introduced to generate unstructured hybrid meshes that fulfil this requirement. Copyright © 2008 John Wiley & Sons, Ltd.     

Velocity–pressure integrated versus penalty finite element methods for high-Reynolds-number flows

Velocity–pressure integrated and consistent penalty finite element computations of high-Reynolds-number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity-pressure integrated method, yields accurate computational results for high-Reynolds-number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity–pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow of Reynolds number 10 000, a laminar backward-facing step flow and a laminar flow through a nest of cylinders.     

Estimate of the truncation error of finite volume discretization of the Navier–Stokes equations on colocated grids

A methodology is proposed for the calculation of the truncation error of finite volume discretizations of the incompressible Navier–Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier–Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretizations of the incompressible Navier–Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure part of the mass fluxes is not dependent on the coefficients of the linearized momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two‐dimensional flows, but extension to three‐dimensional cases should not pose problems. Copyright © 2005 John Wiley & Sons, Ltd.     

高层双塔楼绕流风场效应的数值预测

在一高层双塔楼静力风载风洞试验的基础上,采用时均数值模拟的方法,对其绕流风场进行了模拟,获得了风场的绕流特点和塔楼表面风压的分布规律．通过风压的模拟计算值与试验值的比较,表明以数值方法预测气动干扰强烈的绕流风场是准确和可行的．     

OVERLAPPING GRIDS FOR THE SIMULATION OF PARTICLE INTERACTION AT THE MICRO SCALE

This paper describes the use of overlapping grids for the calculation of flow around single and multipleparticle configurations at the micro scale. The basic equations for calculation are those for conservation of mass and momentum which are solved using a common Finite-Volume formulation. The hydrodynamic particle-particle and particle-wall interaction can be calculated by using an overlapping or Chimera grid scheme. With the grid structuring procedure it is possible to use simple and structured grids around the particles and the overall main grid geometry. The particle grids are lapped over the main grid such that they can move independently after each time step without remeshing the whole geometry. The paper gives results for the validation of the code developed for general test cases, for a rotating ellipsoid in simple shear flow, the flow around particles attached to a wall, the motion of a particle in the vicinity of a wall and some results for the flow through a packed bed configuration.