Navier－Stokes方程与湍流研讨会

Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程与湍流研讨会（１９９５年１２月１８—２１日,北京）在国家科委攀登计划“非线性科学”项目首席专家谷超豪院士的倡议下,由郑哲敏院土、了夏畦院士主持,中科院非线性连续介质力学开放研究实验室承办的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程与...      

Navier—Stokes方程区域分解法：应用及数值模拟

本文构造了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的最优控制区域分解方法的极小化序列,将非线性问题转化为在各子区域上并行求妥一系列线问题。     

不可压缩湍流非对称脱体涡流场数值分析

采用拟压缩性方法，Ｂｅａｍ－Ｗａｒｍｉｎｇ近似因式分解格式数值求解三维定常不可压Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程。对Ｂａｌｄｗｉｎ－Ｌｏｍａｘ代数湍流模型，采用Ｄｅｇａｎｉ－ｓｃｈｉｆｆ修正。计算绕尖头正切拱型旋成柱体的大迎角大雷诺数脱体涡流场，计算结果中的非对称脱体涡与实验相符．     

关于近似惯性流形及其数值方法的研究

本文简述了近年来在无穷维动力系统研究中一些数学理论的进展状况,主要目的是结合二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程讨论近似惯性流形及其数值方法的构造和意义．      

旋涡与水面相互作用研究

采用Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的有限差分数值解来研究水下生成的旋涡在浮升过程中与水面的相互作用，旋涡的初始模型为Ｏｓｅｅｎ涡。数值模拟给出了在旋涡与水面相互作用过程中，水面形状和涡量场的演化，还讨论了Ｆｒｏｕｄｅ数、Ｒｅｙｎｏｌｄｓ数和Ｗｅｂｅｒ数对水面变形的影响。     

血液入口段两相流动的层流NS方程数值模拟

本文采用球形刚性颗粒悬浮于牛顿流体的血液模型，基于有相间滑移的两相流动层流Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，采用相间滑移算法（Ｉｎｔｅｒ－ＰｈａｓｅＳｌｉｐＡｌｇｏｒｉｔｈｍ）对圆管内定常轴对称血液入口两相流动问题进行了计算，获得了与实验结果吻合的计算结果，较好地模拟血液流动中红细胞的径向迁移现象，结果表明，采用二相流动模型研究血液流动是一种有前途的方法。     

透平叶栅跨音速流动计算中的新型有限元法

将Ｔａｙｌｏｒ－Ｇａｌｅｒｋｉｎ有限元法和多级有限元的思想结合起来，构成了在收敛速度和稳定性两方面均较好的新型有限元算法：多级广义有限元。利用这一方法，分别基于Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和Ｅｕｌｅｒ方程，研究了透平跨音速叶栅无粘流动和粘性流动，并将计算结果与实验结果作了比较。计算结果表明，本方法是透平机械内部跨音速流动计算的强有力的手段。     

平行涡管三维合并的直接数值模拟

采用拟谱方法求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，对两个同向平行涡管的三维合并过程进行直接数值模拟，分析了它的不同于二维合并的“缠绕式”特性，特别地，对在合并过程中产生的垂直于初始涡管方向的非主体涡量的意义和物理机制了探讨。     

桥梁主梁断面气动特性计算

采用雷诺平均Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和在连续方程增加压力对时间导致数项的拟压缩性方法，计算桥梁主梁断面气动特性，数值计算过程采用基于中心差分近似和Ｒｕｎｇｅ－Ｋｕｔｔａ时间推进的格点有限体积多重网格法，湍流模式采用Ｂａｌｄｗｉｎ－Ｌｏｎｍａｘ代数模式，以虎门桥主梁断面计算为例，计算的空气动力特性与风洞试验数据吻合很好，本文方法具有占机内存小，计算时间短的优点。     

平面Poiseuille流动力系统稳定性分析

本文把平面Ｐｏｉｓｅｕｉｌｌｅ流的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程化为一非线性动力系统,用线性稳定性理论对其进行分析研究,得到一组特征方程,对离散后的特征方程施加一个矩阵变换,计算出不同波数下的临界雷诺数并与Ｏｒｓｚａｙ和Ｔｈｍｏａｓ的计算结果进行比较,最后画出了Ｐｏｉｓｅｕｉｌｌｅ流的中性稳定性曲线。     

Approximate nonreflecting inflow-outflow boundary conditions for the calculation of navier-stokes equations in internal flows

In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effectiveness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems. recommended by Prof. Cui Erjie     

Unitive analysis schemes on problems of multiple moving boundaries with 3-D liquid-solid multiple nonlinear coupling for uplift of anchored liquid storage tanks

I.Intr0ducti0nAnchored1iquidstoragetanksareextensivelyusedinbusiness,nuclearpowerplants,spaceflightandpetrochemicalindustry.Theystoragepetrochemicalproductions0fover9Opercentintheworld.Theanchoredliquidstoragetanksarecontinuelydamagedduringearthquakestoha…     

Boundary condition formulation for viscous fluid flow problems

In the solution of the Navier-Stokes equations by difference methods in infinite regions, the question arises as to the nature of the approximate boundary conditions at those portions of the computational region boundary where these conditions are not determined directly by the formulation of the basic problem. In certain cases of practical importance, these boundary conditions may be obtained by coupling the N-S equations with equations which are similar to the boundary-layer equations.In the present paper, we propose boundary conditions for the case of viscous incompressible fluid flow. Their application is illustrated for the problem of flow past the leading edge of a semi-infinite flat plate.The author wishes to thank I. Yu. Brailovskaya and L. A. Chudov for helpful suggestions in the course of this investigation.     

A stability study of Navier-Stokes equations (III)

In this paper, the necessary conditions of the existence of C² solutions in some initial problems of Navier-Stokes equations are given, and examples of instability of initial value (at t=0) problems are also given. The initial value problem of Navier-Stokes equation is one of the most fundamental problem for this equation various authors studies this problem and contributed a number of results. J. Lerav, a French professor, proved the existence of Navier-Stokes equation under certain defined initial and boundary value conditions. In this paper, with certain rigorously defined key concepts, based upon the basic theory of J. Hadamard partial differential equations¹, gives a fundamental theory of instability of Navier-Stokes equations. Finally, many examples are given, proofs referring to Ref. [4].     

On the implementation of symmetric and antisymmetric periodic boundary conditions for incompressible flow

In this paper we consider symmetric and antisymmetric periodic boundary conditions for flows governed by the incompressible Navier-Stokes equations. Classical periodic boundary conditions are studied as well as symmetric and antisymmetric periodic boundary conditions in which there is a pressure difference between inlet and outlet. The implementation of this type of boundary conditions in a finite element code using the penalty function formulation is treated and also the implementation in a finite volume code based on pressure correction. The methods are demonstrated by computation of a flow through a staggered tube bundle.     

Two methods of approximate description of steady-state motions of a viscous incompressible liquid with a free boundary

In this paper waves on the surface of a viscous incompressible liquid are investigated in a linear approximation. It is shown that the linear theory gives the principal term of the solution of the problem of steady-state two-dimensional waves of small amplitude in an exact formulation. Subsequently a three-dimensional steady-state motion of a viscous liquid with high surface tension in a vessel is considered. In the first approximation the free boundary is determined as a minimum surface in a field of gravity. The velocity field is found from the solution of the Navier-Stokes equations.     

Navier-Stokes equations with imposed pressure and velocity fluxes

Boundary value problems for Stokes and Navier-Stokes equations with non-standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non-standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier-Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiological flows.     

Advances in the study of separated flows

This paper consists of three parts. The first deals with the separation conditions for three dimensional steady viscous separated flows, in which the behaviour of separated flow described by Navier-Stokes equations and boundary layer equations is studied. The second part involves an application of differential topology to qualitative analysis of flow fields. Here the distribution rule of singular points on the separation line is studied. The last part discusses the numerical method solving Navier-Stokes equations for separated flows. The obtained computational results are analysed by the above mentioned theories and methods.     

Navier-Stokes方程二阶速度滑移边界条件的检验

对微尺度气体流动,Navier-Stokes方程和一阶速度滑移边界条件的结果与实验数据相比,在滑移区相互符合,在过渡领域则显著偏离.为改善Navier-Stokes方程在过渡领域的表现,有些研究者尝试引入二阶速度滑移边界条件,如Cercignani模型,Deissler模型和Beskok-Karniadakis模型.以微槽道气体流动为例,将Navier-Stokes方程在不同的二阶速度滑移模型下的结果与动理论的直接模拟Monte Carlo(DSMC)方法和信息保存(IP)方法以及实验数据进行比较.在所考察的3种具有代表性的二阶速度滑移模型中,Cercignani模型表现最好,其所给出的质量流率在Knudsen数为0.4时仍与DSMC和IP结果相符;然而,细致比较表明,Cercignani模型给出的物面滑移速度及其附近的速度分布在滑流区和过渡领域的分界处(Kn=0.1)已明显偏离DSMC和IP的结果.