定常Stokes问题的边界积分方程法

1.前言 定常Stokes问题本身虽然只反映在小雷诺数情况下不可压缩粘性流体的定常流动,然而却为处理完整的Navier-Stokes方程奠定了基础. Stokes问题一般有两种公式化途径,一是通过流函数,二是利用速度-压力公式.两种公式化途径的区域类型数值方法,如有限差分法及有限单元法,已有不少工作,见[3]和[11].近年来,对这两种公式化途径的边界类型数值方法的研究,也获得一些结果.     

中医滚法推拿对血液流动影响的数值研究

研究了中医滚法推拿的血液动力学机制．用狭窄轴向运动来模拟滚法推拿,通过轴对称非线性模型和含网格重分算法的任意欧拉-拉格朗日有限元方法研究狭窄轴向运动的轴对称刚性管中的粘性流动．流量和管壁切应力通过数值求解Navier-Stokes方程得到．数值结果表明,狭窄运动的频率,也就是滚法推拿的频率对流量和管壁切应力有很大的扰动作用．滚法推拿中另一个可变参数——刻划狭窄严重程度的狭窄度,对流量和管壁切应力同样表现出显著影响．这些数值结果可以为推拿的临床应用提供一些值得参考的数据．     

动脉血管流动计算的伽辽金有限元法研究

得到大动脉三维模型的过二重分叉的二维截定常流的NS方程有限元解,采用了物理坐标系统换到曲线边界贴休坐标系的数学技巧,以支流至主动脉流率为参数,计算了雷诺数为1000的壁面切应力,所得结果与前人的工作（包括实验数据）进行了比较,发现与他们的结果非常接近,改进了Sharma和Kapoor(1995)的工作,相比之下,所用的数值方法上更经济,适用的雷诺数更大。     

锥形血管入口区域内管壁应力分析

本文对锥形血管入口区域的流动进行了探讨，导出了压力分布、轴向和径向的速度分布以及流场的切应力分布、管壁应力分布等公式，进行了相应的数值算例的研究和分析，还着重讨论了血管锥度角对管壁应力、压力分布等的影响。     

求解二维不可压缩Navier-Stokes方程的混合型微分求积法

微分求积法（ＤＱＭ）能以较少的网格点求得微分方程的高精度数值解,但采用单纯的微分求积法求解二维不可压缩Ｎａｖｉｅｒ＿Ｓｔｏｋｅｓ 方程时,只能对低雷诺数流动获得较好的数值解,当雷诺数较高时会导致数值解不收敛·　为此,提出了一种微分求积法与迎风差分法混合求解二维不可压缩Ｎａｖｉｅｒ＿Ｓｔｏｋｅｓ 方程的预估＿校正数值格式,用伪时间相关算法以较少的网格点获得了较高雷诺数流动的数值解·　作为算例,对１∶１ 和１∶２ 驱动方腔内的流动进行了计算,得到了较好的数值结果·     

定常无粘超音速绕流计算的一些数值结果

本文介绍用稳定法计算球锥、抛物头一柱、平头锥、烧蚀外形物体、三角机翼、翼身组合体等物体的定常无粘超音速绕流的数值方法,并用图表显示了诸类外形在几个典型状态下的数值结果。     

对流扩散方程的高效稳定差分格式

基于二阶修正Dennis格式 ,提出了采用时间相关法求解定常对流扩散方程的一种具有节省内存空间和提高定常解收敛速度的有理式型优化半隐和松驰半隐紧致格式 .本文建立的差分格式具有运算量小、无网格雷诺数限制的优点 ,是无条件稳定和无条件单调的。通过对非线性Burgers方程进行的数值计算结果表明 ,文中构造的有理式型优化半隐和松驰半隐紧致格式适合于非线性问题计算 ,且保持了无条件稳定和无条件单调的特性 ,尤其能使定常解收敛速度加快 ,精度提高 .     

T型分叉血管的定常/脉动流动和大分子传质

采用计算流体动力学方法,数值求解了T型分叉流动的定常/脉动流场和低密度脂蛋白(LDL)以及血清白蛋白(Albumin)的浓度分布。计算了雷诺数、主管和支管的流量比等参数对流场和大分子传质的影响,计算结果表明,流体动力学因素影响大分子的分布和跨壁渗透,在动脉硬化的发生和发展过程中起着重要的作用。在流动发生分离处,即支管入口外侧壁面剪应力变化最剧烈,这儿LDL和Albumin的壁面浓度变化也是最剧烈,是动脉硬化危险区。     

动脉管壁切应力的确定

血管为了适应所处力学环境的变化会产生结构和功能的变化,血液流动作用于血管壁上的切应力在这种血管重建中起着重要的作用.目前直接测量活体血管壁切应力存在着许多技术上的困难.通过分析动脉中血液脉动流的特性,提出一种利用测量管轴上的血流速度,计算血管壁切应力的方法,为定量确定血管壁切应力,进而讨论血管壁切应力对血管重建的影响提供必要的手段.     

恒定不可压缩Couette流的通用理论——Ⅰ.流场中存在零切应力平面这种情况

本文对具有零切应力平面这类科特流的计算提出了一种新的普遍的方法。该方法利用了Couette流与槽道流的动力相似性,推出了六个Couette流的参数方程:即二壁面切应力,流速极点及其坐标的方程,并据此可求得切应力与流速的分布。这个方法不需要采用混合长及紊流粘性系数假说,唯一需要的是槽道流摩擦系数与流速分布的知识。还提出了一个新的Couette流的相似准则——Couette数P.这些方程曾在广泛的范围内进行过示例计算和实验印证,这部分内容将在另文介绍。     

Numerical computation of pulsatile flow through a locally constricted channel

This paper deals with the numerical solution of a pulsatile laminar flow through a locally constricted channel. A finite difference technique has been employed to solve the governing equations. The effects of the flow parameters such as Reynolds number, flow pulsation in terms of Strouhal number, constriction height and length on the flow behaviour have been studied. It is found that the peak value of the wall shear stress has significantly changed with the variation of Reynolds numbers and constriction heights. It is also noted that the Strouhal number and constriction length have little effect on the peak value of the wall shear stress. The flow computation reveals that the peak value of the wall shear stress at maximum flow rate time in pulsatile flow situation is much larger than that due to steady flow. The constriction and the flow pulsation produce flow disturbances at the vicinity of the constriction of the channel in the downstream direction.     

Accelerated slip flow past a cylinder

This study deals with boundary layer flow along the entire length of a stationary semi-infinite cylinder under a steady, accelerated free-stream. Considering flow at reduced dimensions, the no-slip boundary condition is replaced with a Navier boundary condition. Asymptotic series solutions are obtained for the shear stress coefficient in terms of the Bingham number that corresponds to prescribed values of both the slip coefficient and the index of acceleration. By investigating motion at small and large axial distances, the series solutions are presented. For flow in the intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the shear stress along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.     

Accelerated slip flow past a cylinder

This study deals with boundary layer flow along the entire length of a stationary semi-infinite cylinder under a steady, accelerated free-stream. Considering flow at reduced dimensions, the no-slip boundary condition is replaced with a Navier boundary condition. Asymptotic series solutions are obtained for the shear stress coefficient in terms of the Bingham number that corresponds to prescribed values of both the slip coefficient and the index of acceleration. By investigating motion at small and large axial distances, the series solutions are presented. For flow in the intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the shear stress along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.     

Steady and Unsteady Jet Wiping Processes

The jet wiping process is widely used in continuous coating applications to remove the excess amount of liquid entrained by a sheet moving out of a liquid bath. Typical fields of applications are hot dip galvanization of metal strips and coating of photographic films. The process is based on the impact of a gas jet onto the liquid film carried by the solid substrate. In the present study the process is investigated for the case of strictly two‐dimensional flow. It is assumed that inertia effects on the film flow can be neglected, whereas the effects of the pressure gradient and the shear stress distribution of the impinging jet and the surface tension of the liquid film are taken into account. As a result it is possible to derive a single kinematic wave equation which governs the distribution of the film thickness. Numerical results for representative steady and unsteady processes including the formation of shock discontinuities are presented.     

Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains

We prove that, in a two‐dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half‐plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on one‐dimensional symmetry results for solutions of some semilinear elliptic equations. Some related rigidity results of independent interest are also shown in n‐dimensional slabs in any dimension n.© 2016 Wiley Periodicals, Inc.     

Analysis of wavy flow and blood oxygenation in two-dimensional channels with constriction

A steady wavy incompressible Newtonian fluid flow in a channel with irregular surfaces is studied to understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels. Analytical solutions are obtained under the assumption that the spread of the surface roughness to be large compared to the mean width of the channel. Expressions for the stream function, vorticity, the wall shear stress distribution and viscous energy loss per unit cycle are derived and the effects of various pertinent parameters upon them have been investigated for symmetric and non-symmetric channels with graphical representations. In order to determine the effects of the wall roughness upon the blood oxygenation in a membrane oxygenator, the haemodynamical solution is used. It is found that oxygen concentration increases with increase of channel constriction due to increase of cell-plasma and cell-cell interaction as well as waviness of flow field and this is predicted graphically.     

Blasius flow of thixotropic fluids: A numerical study

In the present work, laminar, two-dimensional flow of an incompressible thixotropic fluid obeying Harris rheological model is investigated above a fixed semi-infinite plate- the so-called Blasius flow. Assuming that the flow is occurring at high Reynolds number, use will be made of the boundary layer theory to simplify the equations of motion. The equations so obtained are then reduced to a single fourth-order ODE using a suitable similarity variable. It is shown that Harris fluids do not render themselves to a self-similar solution in Blasius flow. A local similarity solution is found which enabled investigating the effects of the model parameters on the velocity profile and wall shear stress at a given location above the plate. Numerical results show that for the Harris model to represent thixotropic fluids, the sign and magnitude of the material parameters appearing in this fluid model cannot be arbitrary.     

Crocco variable formulation for uniform shear flow over a stretching surface with transpiration: Multiple solutions and stability

The simultaneous effects of transpiration through and tangential movement of a semi-infinite flat plate on the self-similar boundary layer flow driven by uniform shear in the far field is considered. Difficulties with standard shooting techniques are overcome using Crocco variables which also serve to better elucidate the solution structure. The stabilities of dual, triple and even quadruple steady flow solutions encountered in different ranges of plate stretching and wall stress are determined using a linear temporal stability analysis for the self-similar flow.      

Instability of power-law fluid flows down an incline subjected to wind stress

In this paper we investigate the effect of a prescribed superficial shear stress on the generation and structure of roll waves developing from infinitesimal disturbances on the surface of a power-law fluid layer flowing down an incline. The unsteady equations of motion are depth integrated according to the von Kármán momentum integral method to obtain a non-homogeneous system of nonlinear hyperbolic conservation laws governing the average flow rate and the thickness of the fluid layer. By conducting a linear stability analysis we obtain an analytical formula for the critical conditions for the onset of instability of a uniform and steady flow in terms of the prescribed surface shear stress. A nonlinear analysis is performed by numerically calculating the nonlinear evolution of a perturbed flow. The calculation is carried out using a high-resolution finite volume scheme. The source term is handled by implementing the quasi-steady wave propagation algorithm. Conclusions are drawn regarding the effect of the applied surface shear stress parameter and flow conditions on the development and characteristics of the roll waves arising from the instability. For a Newtonian flow subjected to a prescribed superficial shear stress, using an analytical theory, we show that the nonlinear governing equations do not admit roll waves solutions under conditions when the uniform and steady flow is linearly stable. For the case of a general power-law fluid flow with zero shear stress applied at the surface, the analytical investigation leads to a procedure for calculating the characteristics of a roll waves flow. These results are compared with those yielded by the numerical procedure.