对流-扩散相互作用结构的不变性

本文提出并证明了不可压缩剪切层流中对流-扩散相互作用结构不变性诸定理:即二难剪切层流与其线性化及非线性扰动存在同一的对流-扩散相互作用结构,且物理尺度(指时间、空间和速度尺度)相同。给出十个推论,例如:对流-扩散相互作用可在剪切层流及其扰动场内“激发“快时间尺度和小空间尺度结构,线性化稳定性原理的约定对剪切流体系统成立等。应用题例导出计及时间-空间尺度效应和非平行流效应的广义Orr-Sommerfeld(GOS)方程,证实它有两个粘性解:阻尼层解和干扰层解;经典OS方程及其两个粘性解:边界层解和Heisenberg临界层解,Triple-deck稳定性理论基本方程及其两个粘性解,均是本文GOS方程及其两个粘性解的特例。     

非平整运动海底上n层流动中波浪传播的Hamilton逼近

在海洋水域，界面波对大尺度变化流的作用是一种典型的分层流动现象．考虑一不可压缩、无黏的分层势流运动，建立了一个在非平整运动海底上的n层流体演化系统，并对其进行了Hamilton描述．每层流体具有各自的常密度、均匀流水平速度，其厚度由未扰动和扰动部分构成．相对于顶层流体的自由表面，刚性、运动的海底具有一般地形变化特征．在明确指出n层流体运动的控制方程和各层交界面上的运动学、动力学边界条件(包含各层交界面上张力效应)后，对该分层流动力系统进行了Hamilton构造，即给出其正则方程和其下述的正则变量：各交界面位移和各交界面上的动量势密度差。     

圆柱绕流教学中常被忽略的一个问题

<正> 笔者所见不少流体力学教材在讲述无环量圆柱绕流时,大都这样处理:1)推出速度势(?)(或流函数(?))满足的 Laplace 方程 ▽~2(?)=0(或▽~2(?)=0);2)给出若干个基本解;3)将均匀流与偶极子两个基本解叠     

位势流动和非均匀介质中声波方程的36种形式

声波方程是对大多数声学问题进行数学描述的出发点. 那些得到 广泛应用的经典波动方程及对流波动方程都存在苛刻的适用条件, 即仅适用于描述处于静态或匀速运动状态的定常 均匀介质中的线性无耗散声波. 然而, 很多实际场合并不满足这些严格的适用条件. 本文对经典声波方程和对流声波 方程进行推广, 导出了编号为W1$\sim$W36的36种不同形式的声波方程, 涵盖了处于静止、势流或旋涡流状态下的非均匀 和/或非定常介质中的声波传播问题. 所考虑的声波传播情形包括: (1) 线性波, 即具有小梯度(小振幅)性质; (2)非线性波, 即具有陡峭梯度性质, 包括``波纹'(小振幅大梯度)或者大振幅波. 本文仅考虑非耗散声波, 即排除了由剪切、体积黏度及热传导所引起的耗散. 对具有匀熵或等熵(熵沿流线守恒)性质的均匀介质和非均匀介质中的声传播进行了研究但非等熵(即耗散)情况除外; 另外, 对非定常介质中的 声波问题也进行了分析. 所涉及的介质可以处于静止、匀速运动状态, 或者是非匀速的和/或非定常的平均流动, 包括: (1)低Mach数的势平均流(即不可压缩的平均态), 或高速势平均流(即非均匀可压缩的平均流); ② 变截面管 道中的准一维传播, 包括无平均流的号管和具有低或高Mach数平均流的喷管; 或③平面的、空间的、或轴对称的单 向剪切平均流. 本文没有探讨其他类型的旋涡平均流(将与耗散及其他情形一起留待下一步研究), 例如, 可能与剪切效应相结合的轴对称旋转平均流. 通过对流体力学的一般方程进行消元处理或根据声学变分原理, 导出了36种波动方程, 对一些波动方程还采用这两种方法进行相互校验. 尽管声波方程的36种形式没有涵盖非线性、非均匀与非定常及非匀速运动介质 这3个效应的所有可能的组合情形, 但它们的确包括了孤立状态下的各种效应, 并包括了多种多重效应组合的 情形. 虽然经典波动方程和对流波动方程仅适用于处于静止(或匀速运动)的均匀定常介质中的线性无耗散声波, 但它们在 相关文献中已被广泛采用; 本文给出的36种声波方程提供了它们多种有用的推广形式. 在许多实际应用中, 经典波动方 程和对流波动方程仅是粗略的近似, 声波方程的更一般形式可提供更令人满意的理论模型. 本文每节末尾给出了这些应用 的众多范例. 在这篇评论文章中引用了240篇参考文献.     

一种寻求层状流动新解的方法

复杂层状流动是流体力学中的一类典型的流动。一般而言，流体力学中有两种特殊的流动：一种是Beltrami流动，另一种就是层状流动。对于前者，已经讨论过很多；但是后者的精确解却很难获得，这是因为很难解这种流动的Navier-Stokes方程或Euler方程。从不可压缩条件出发，如果让速度的形式满足一些特殊的条件，可以得到关于这种流动的某些新的精确解，例如发现一种间歇流精确解。     

应用跨音速高级近似扰动速势方程计算钝前缘翼型的压力分布

本文在文献[1,2]的基础上进一步采用较高级的近似扰动速势方程来计算钝前缘翼型的跨音速压力分布。所采用的速势方程是式中μ=0为一级近似扰动速势方程,μ=1为高级近似扰动速势方程。扰动参数ε_1=δ~2/~3/M_(∞ο)在翼型的钝前缘点处采用精确速势方程     

简化Navier-Stokes方程组(SNSE)的几个精确解

对不可压二维驻点流、三维驻点流和旋转圆盘附近的流动等三种流动情况,本文给出简化Navier-Stokes方程组(SNSE)及其精确解。表明:文献[1]理论的SNSE的精确解,在三种流动情况下均与完全Navier-Stokes方程组(NSE)的精确解完全一致;文献[3]SNSE的精确解的速度解与完全NSE精确解的速度解一致,但压力解在三种流动情况下均与完全NSE精确解的压力解不同。文献[3]SNSE精确解给出的压力分布相对与完全NSE精确解给出的压力分布的最大相对误差为100％。     

行进间瞄准线稳定技术

针对两自由度稳瞄转台提出了行进间瞄准线两级稳定策略。为了克服稳瞄转台基座扰动对瞄准线的影响，利用微陀螺惯性测量组合(MEMIMU)测量出六个扰动参数(三个平动以及三个转动)，解算出瞄准线新的方位与俯仰值，实现第一级稳定；然后利用CCD成像技术，通过操作员控制方向手柄，使得瞄准线稳定地跟踪上机动目标。该技术特别适合于海况中精确瞄准问题以及晃动基座情况下的定向通讯稳定等。     

二阶非牛顿流体蠕流精确解

二阶流体是工业界常见的非牛顿流体,因为其本构关系简单而被广泛采用和研究.逆方法预先假定流场满足某类特定的物理的或几何的特性,从而求出流体运动方程的精确解.本文通过假定平面定常二阶非牛顿流体的涡量场与受到扰动的流函数相等这一特定形式,采用求解非线性微分方程常用的逆方法,推导并获得了平面二阶蠕流流场的精确解,由此容易进一步获得流场的压力.所获得的精确解包含了Poiseuille,简单Couette平行流动以及两相向流体的相互作用等流动.这些精确解为实验,数值以及渐进解的检验提供了借鉴和参考.     

炮孔之间爆炸应变场的光力学分析

本文分别运用动态云纹-光弹性和电阻应变量测方法研究了相邻两炮孔之间爆炸应变场。多火花式高速像机和超动态量测系统被用于动态记录。根据动态云纹-光弹条纹分析了应力波的叠加作用,定量地计算了爆炸应力波叠加作用期间内不同时刻地孔连心线上_x(沿连心线方向)和_r(垂直于连心线方向)的分布以及_x在连心线中垂线上的分布。用应变片记录了爆炸应力波叠加作用时连心线上应变-时间示波器轨迹。测量和计算所得炮孔间应力波叠加和衰减的规律与理论分析和动光弹模拟分析结果一致。     

General exact solution of incompressible potential flows around two circles

Three exact solutions are obtained for 2-D incompressible potential flows around two moving circles in three cases: (i) expansion (or contraction) of themselves, (ii) approaching (or departing from) each other, (iii) moving perpendicularly to the line connecting the centres in opposite directions. Meanwhile, another set of two exact solutions is obtained for 2-D incompressible potential flows between two moving eccentric circles in two cases: moving parallely or perpendicularly to the line connecting the centres.     

用三维半人工瞬变法计算圆管内圆柱绕流

本文提出一种计算三维定常流动的半人工瞬变法,本方法的特点是直接利用流体力学的原始基本方程组进行数值计算。运动方程中的一个分量方程被用于计算压力,另外两个分量方程被加入人工瞬变项而成为人工瞬变方程,这两个人工瞬变方程被用于计算速度的两个分量,第三个速度分量则通过连续性方程进行计算得到。根据半人工瞬变方程组的特点和流动区域的特性,本方法采用半交错不等距非正交曲线贴体混合网格系进行数值计算,并利用质点导数差分格式使计算更简便。本文以圆管中不可压缩流体对圆柱的三维定常绕流问题为算例,具体画出计算用的半交错不等距非正交曲线贴体混合网格系,介绍三维半人工瞬变法的计算方法和步骤,并通过数值计算得到了此算例的计算结果。     

The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces

Numerical modeling of the melting and combustion process is an important tool in gaining understanding of the physical and chemical phenomena that occur in a gas‐ or oil‐fired glass‐melting furnace. The incompressible Navier–Stokes equations are used to model the gas flow in the furnace. The discrete Navier–Stokes equations are solved by the SIMPLE(R) pressure‐correction method. In these applications, many SIMPLE(R) iterations are necessary to obtain an accurate solution. In this paper, Krylov accelerated versions are proposed: GCR‐SIMPLE(R). The properties of these methods are investigated for a simple two‐dimensional flow. Thereafter, the efficiencies of the methods are compared for three‐dimensional flows in industrial glass‐melting furnaces. Copyright © 2000 John Wiley & Sons, Ltd.     

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

This paper presents a local moving least square‐one‐dimensional integrated radial basis function networks method for solving incompressible viscous flow problems using stream function‐vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square and one‐dimensional integrated radial basis function networks techniques. The major advantages of the proposed method include the following: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker‐ δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local radial basis function approximations. Several examples including two‐dimensional (2D) Poisson problems, lid‐driven cavity flow and flow past a circular cylinder are considered, and the present results are compared with the exact solutions and numerical results from other methods in the literature to demonstrate the attractiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Time‐dependent flow across a step: the slip with friction boundary condition

The paper studies numerically the slip with friction boundary condition in the time‐dependent incompressible Navier–Stokes equations. Numerical tests on two‐ and three‐dimensional channel flows across a step using this boundary condition on the bottom wall are performed. The influence of the friction parameter on the flow field is studied and the results are explained according to the physics of the flow. Due to the stretching and tilting of vortices, the three‐dimensional results differ in many respects from the two‐dimensional ones. Copyright © 2005 John Wiley & Sons, Ltd.     

Three‐dimensional transient free‐surface flow of viscous fluids inside cavities of arbitrary shape

The three‐dimensional transient free‐surface flow inside cavities of arbitrary shape is examined in this study. An adaptive (Lagrangian) boundary‐element approach is proposed for the general three‐dimensional simulation of confined free‐surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free‐surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free‐surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. The method is used to determine the flow field and free‐surface evolution inside cubic, rectangular and cylindrical containers. These problems illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored. Copyright © 2003 John Wiley & Sons, Ltd.     

A simple incompressible flux splitting for sharp free surface capturing

This paper first applies a flux vector‐type splitting method based on the numerical speed of sound for computing incompressible single and multifluid flows. Here, a preconditioning matrix based on Chorin's artificial compressibility concept is used to modify the incompressible multifluid Navier–Stokes equations to be hyperbolic and density or volume fraction‐independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratios and enhance numerical stability. Also, a simple convection‐pressure flux‐splitting method with high‐order essentially nonoscillatory‐type primitive variable extrapolations coupled with monotone upstream‐centered schemes for conservation laws‐type volume fraction recompressed reconstruction is used to maintain the preservation of sharp interface evolutions in multifluid flow simulations. Benchmark tests including a solid rotation test of a notched two‐dimensional cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, and the Rayleigh–Taylor instability were chosen to validate the current incompressible multifluid methodology. An incompressible driven cavity was also chosen to check the robustness of the proposed method on the computation of single fluid incompressible flow problems. Copyright © 2011 John Wiley & Sons, Ltd.     

High‐order compact scheme for Boussinesq equations: implementation and numerical boundary condition issue

Application of the three‐point fourth‐order compact scheme to spatial differencing of the vorticity‐stream function‐density formulation of the two‐dimensional incompressible Boussinesq equations is presented. The details for the derivation of difference relations at boundaries to generate accurate and stable solutions are also given. To assess the numerical accuracy, two linear prototype test problems with known exact solution are used. The two‐dimensional planar and cylindrical lock‐exchange flow configurations are used to conduct the numerical experiments for the Boussinesq equations. Quantitative measures for the two linear prototype test problems and comparison of the results of this work with the published results for the planar lock‐exchange flow indicates the validity and accuracy of the three‐point fourth‐order compact scheme for numerical solution of two‐dimensional incompressible Boussinesq equations. In addition, the study of using different high‐order numerical boundary conditions for the implementation of the no‐penetration boundary condition for the density at no‐slip walls is considered. It is shown that the numerical solution is sensitive to the choice of difference relation for the density at boundaries and using an inappropriate difference relation leads to spurious numerical solution. Copyright © 2011 John Wiley & Sons, Ltd.     

A dimension split method for the incompressible Navier–Stokes equations in three dimensions

In this paper, we describe a new method for the three‐dimensional steady incompressible Navier–Stokes equations, which is called the dimension split method (DSM). The basic idea of DSM is that the three‐dimensional space is split up into a cluster of two‐dimensional manifolds and then the three‐dimensional solution is approximated by the solutions on these two‐dimensional manifolds. Through introducing some technologies, such as SUPG stabilization, multigrid method, and such, we firstly make DSM feasible in the computation of real flow. Because of split property of DSM, all computation is carried out on these two‐dimensional manifolds, namely, a series of two‐dimensional problems only need to be solved in the computation of three‐dimensional problem, which greatly reduces the difficulty and the computational cost in the mesh generation. Moreover, these two‐dimensional problems can be computed simultaneously and a coarse‐grained parallel algorithm would be constructed, whereas the two‐dimensional manifold is considered as the computation unit. In the last, we explore the behavior and the accuracy of the proposed method in two numerical examples. Firstly, error estimates, performance of multigrid method, and parallel algorithm are well‐demonstrated by the known analytical solution case. Secondly, the computations of three‐dimensional lid‐driven cavity flows with different Reynolds numbers are compared with other numerical simulations. Results show that the present implementation is able to exhibit good stability and accuracy properties for real flows. Copyright © 2013 John Wiley & Sons, Ltd.     

A stable and accurate projection method on a locally refined staggered mesh

In this paper, a robust projection method on a locally refined mesh is proposed for two‐ and three‐dimensional viscous incompressible flows. The proposed method is robust not only when the interface between two meshes is located in a smooth flow region but also when the interface is located in a flow region with large gradients and/or strong unsteadiness. In numerical simulations, a locally refined mesh saves many grid points in regions of relatively small gradients compared with a uniform mesh. For efficiency and ease of implementation, we consider a two‐level blocked structure, for which both of the coarse and fine meshes are uniform Cartesian ones individually. Unfortunately, the introduction of the two‐level blocked mesh results in an important but difficult issue: coupling of the coarse and fine meshes. In this paper, by properly addressing the issue of the coupling, we propose a stable and accurate projection method on a locally refined staggered mesh for both two‐ and three‐dimensional viscous incompressible flows. The proposed projection method is based on two principles: the linear interpolation technique and the consistent discretization of both sides of the pressure Poisson equation. The proposed algorithm is straightforward owing to the linear interpolation technique, is stable and accurate, is easy to extend from two‐ to three‐dimensional flows, and is valid even when flows with large gradients cross the interface between the two meshes. The resulting pressure Poisson equation is non‐symmetric on a locally refined mesh. The numerical results for a series of exact solutions for 2D and 3D viscous incompressible flows verify the stability and accuracy of the proposed projection method. The method is also applied to some challenging problems, including turbulent flows around particles, flows induced by impulsively started/stopped particles, and flows induced by particles near solid walls, to test the stability and accuracy. Copyright © 2010 John Wiley & Sons, Ltd.