一种改进的分块隐式数值方法

提出了一种改进的分块隐式数值方法，在贴体坐标和交错网格下以逆变速度分量和压力Ｕ，Ｖ，Ｗ，ｐ为基本求解变量，由此克服了原分块隐式数值方法求解复杂边界流动时的困难．９０°弯管流动数值计算初步表明，本文提出的方法合理、可行     

二维流体力学计算中的人为热流方法

采用Ｗ．Ｆ．Ｎｏｈ提出的人为粘性和人为热流方法,构造了计算人为热流的二维差分格式。应用Ｌａｇｒａｎｇｅ型流体力学计算程序,计算了一种二维轴对称高速碰撞模型。计算结果表明,人为热流方法可以很好地消除人为粘性在碰撞界面处的误差。     

简化Navier—Stokes方程的IFT理论的各向异性张力有限元法

本文首先讨论简化Navier-Stokes IFT方程组的有限元离散方式,然后对其广义解进行分析,并从而利用与之相匹配的各向异性张力单元对流函数—涡量方程进行计算。通过平板层流和台阶绕流两个算例的分析,证明这种与IFT理论相匹配的有限单元算法是成功的。     

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.     

Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading

The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configu- rations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain criticM value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.     

Dynamic torsional response of pre-strained end bearing pile embedded in pre-strained isotropic saturated soil medium

The influence of initial strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated through the linearized theory of small elastic perturbation superposed on largely stressed bodies. The governing equations for soil, based on Blot＇s poroelasticity theory, are derived in the cylindrical coordinates, and the pile is modeled by using the one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of both twist angle and time history of velocity response are obtained by using of separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle, and velocity response at the top of the pile is carried out.     

Shocklets in compressible flows

The mechanism of shocklets is studied theoretically and numerically for the stationary fluid, uniform compressible flow, and boundary layer flow. The conditions that trigger shock waves for sound wave, weak discontinuity, and Tollmien-Schlichting （T-S） wave in compressible flows are investigated. The relations between the three types of waves and shocklets are further analyzed and discussed. Different stages of the shocklet formation process are simulated. The results show that the three waves in compressible flows will transfer to shocklets only when the initial disturbance amplitudes are greater than the certain threshold values. In compressible boundary layers, the shocklets evolved from T-S wave exist only in a finite region near the surface instead of the whole wavefront.     

Numerical simulation of motion and deformation of ring bubble along body surface

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.     

Comprehensive form of solution for Lamb＇s dynamic problem expressed by Green＇s functions＊

By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the results of Green＇s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a senti-space, the authors obtain the solutions of Green＇s function for Lamb＇s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb＇s previous results, and the solutions of the linear expansion source u~r and the linear torsional source uee are also given in the paper. The authors reveal that Green＇s function of Stokes＇ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb＇s problem for various situations. It may benefit the investigation of deepening and development of Lamb＇s problems and solution for pertinent dynamic problems conveniently.     

粘性流动动力学有限元变分原理

本文把建立有限元变分原理的一种新方法“Ｎ〉２直接方法”从固体力学推广到流体力学，并用该方法把粘性流体动力学的广义功率消耗原理＾［２］和广义变分原理＾［２］发展成为有限元变分原理。还在论证中发现，相邻有限元交界面上的应力协调条件会自然地满足而无需引进任何拉氏乘子。本文还建立了混合杂交非协调元的变分原理和广义变分原理，它解除了全部协调性约束条件和其它的边界性约束条件，但是并不增加待定的拉氏乘子，因此使     

N表面张力对近固壁二空化泡影响的数值研究

在忽略浮力下,用边界积分方法数值模拟了表面张力对固壁之上且靠近固壁的二轴对称空化泡生长和溃灭的影响,发现在下空泡最大等效半径为上空泡一半情形,若固壁对下空泡的Bjerknes力大于上空泡对下空泡的Bjerknes力,则表面张力的作用将使下空泡溃灭加速,使其向下的液体射流变强变宽;若固壁对下空泡的Bjerknes力小于上空泡对下空泡的Bjerknes力,则表面张力的作用将使下空泡溃灭变慢,使其向上射流变弱变细长;若这两个Bjerknes力近于相等,则表面张力将会对下空泡溃灭有重大作用,如改变下空泡射流的方向甚至形式(如由环状变向下或由向上变环状),当上空泡等于或小于下空泡时,表面张力将不会对这两个空泡的行为产生显著影响,定性地分析了表面张力作用的机理。     

跨声速激波边界层相互作用的被动控制

运用激波管风洞在Ｒ＿（ｅ∞／ｍ＝３×１０￣７，Ｍ＿∞＝０．７３２－０．８１７范围内，在厚度比为１２％的圆弧翼型半模型和厚度比为１４％的超临界翼型半模型上，对被动控制现象及其若干规律进行了实验研究。结果表明，不同空腔深度的开孔壁和导管连通壁均可对壁面激波与边界层的相互作用实现被动控制，使得沿以上两种模型表面的马赫数峰值、逆压力梯度和激波强度明显减小。这对于飞行器将起到减阻作用，如将这一原理和方法用于超、跨声速压气机内激波与边界层相互作用的控制，将提高压气机的效率和工作的稳定性。     

CALCULATION OF STEADY AND OSCILLATING FLOWS IN TUBES USING A VORTICITY TRANSPORT ALGORITHM

Steady and oscillating axisymmetric tube flows are modelled using a vorticity transport algorithm. The axisymmetric convective –diffusive Navier–Stokes equations are solved using a splitting technique. Axisymmetric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equation similar to the Oseen diffusion equation is used to diffuse the ring vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille flow and for the developed flow in the form of the entrance length and the axial velocity and vorticity profiles. Good agreement is achieved with a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solutions. The developed profiles of velocity and vorticity have errors of less than 0ċ3 per cent for both methods of dealing with reflection of diffusion at the bounding surfaces and similar accuracy is obtained for the velocity profiles in oscillating flow except at the wall. Oscillating flow is produced with a discretized sinusoidal piston motion. Velocity profiles, boundary layer thickness and entrance length are presented for oscillating flow. Good agreement is achieved for low-Womersley-number non-dimensional frequency. At higher values of this parameter, flows are inaccurately simulated, because the number of piston positions used to discretize the piston motion is inversely proportional to the non-dimensional frequency.