不可压缩黏性流体的二维Navier-Stokes方程的间断有限元模拟

由于不可压缩Navier-Stokes方程由守恒律、扩散及约束发展方程混合构成,为测试数值方法,该文基于非结构网格,对该方程建立了DG(discontinuous Galerkin)格式,讨论了不同黏性系数ν在方腔涡流问题的数值结果,验证了该方法的有效性且不依赖于问题的维数.圆柱绕流问题的模拟结果进一步表明此方法精度高、可有效求解具有运动界面的不可压缩黏性流体问题,使得模拟边界层、剪切层及复杂涡流解十分有效,并可以成功地推广到解决复杂现象数值模拟中的激波结构.     

求解不定常圆柱绕流的区域分裂法

本文把区域分裂法与涡点格法相结合,以此构造一类并行算法,数值模拟不定常圆柱绕流在高Reynolds数情况下的初期流动. §1.基本问题 假设有一个半径为a的圆柱体,在静止的不可压粘性流体中,以速度U突然起动,此流动满足二维不定常Navier-Stokes无量纲化方程:     

黏性不可压流体的自适应网格技术和基本特性方程分离算法的联合分析

组合基本特性方程分离算法和自适应网格技术,分析二维黏性不可压流体.该方法使用3节点三角单元,对速度分量和压力等变量分析,使用等阶次的插值函数.组合解法的主要优点在于,在自适应网格技术中,对解梯度变化大的区域,通过耦合误差估计生成小的单元,利于提高解的精度,在其它区域生成大单元,可以节省时间.最后,通过对一个黏性流体圆柱体绕流问题的瞬态和稳态特性分析,给出了组合解法性能的评价.     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

含压力基Navier-Stokes方程最优动力系统建模和分析

研究了采用压力基函数和速度基函数的Navier-Stokes方程的最优截断低维动力系统建模理论.在黏性不可压缩流体中模拟了并排三方柱绕流流场,对此流场进行了含压力基函数和速度基函数的Navier-Stokes方程的最优动力系统建模,并以此为工具分析了三方柱绕流最优动力系统的动力学特性.该研究得到了如下结论:三方柱绕流的最优动力系统的动力学行为为混沌,它与双方柱绕流场的极限环动力学特性有着本质的区别,因此可以通过多柱绕流增进尾流的复杂性,从而促进流体混合.     

均匀自由流动的非牛顿流体中连续表面上的磁流体动力学流动和热传递

分析在平行自由流动的非牛顿黏弹性导电流体中,连续平展表面移动时的稳态流和热传递特性,该流动处于横向均匀磁场作用下.以二阶流体构建它的本构方程,得到了速度分布和温度断面图的数值结果.讨论了诸如黏弹性参数、磁场参数和Prandtl数等不同物理参数对诸种动量和热传递特性的影响,并给出相关图示.     

不可压饱和多孔弹性杆动力响应的多辛方法

研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.     

液固两相圆柱绕流尾迹内颗粒扩散分布的离散涡数值研究

基于离散涡方法求得的非定常水流场和颗粒的Lagrange运动方程,数值模拟了稀疏液固两相圆柱绕流尾迹内颗粒的扩散分布．获得了流动的涡谱与3种不同St数颗粒（St=0.25,1.0,40）在流场中的分布．通过引入扩散函数来定量表示颗粒在流场中的纵向扩散强度,并计算得到了不同St数颗粒的扩散函数随时间的变化．数值结果揭示出了液固两相圆柱绕流尾迹中的颗粒扩散分布与颗粒的St数和尾涡结构密切相关:1) 中小St数(St=0.25～4.0)颗粒在运动过程中不能进入涡核区,而在旋涡结构的外沿聚集,且颗粒的St数愈大,其越远离涡核区域;2） 在圆柱绕流尾迹区域内,中小St数(St=0.25～4.0)颗粒的纵向扩散强度随其St数的增大而减小．     

偏斜来流对圆柱跨声速绕流的影响

采用大涡模拟方法数值研究了偏斜角为60°的偏斜圆柱跨声速绕流.基于非偏斜圆柱跨声速绕流的实验和数值研究工作,来流Mach数取为0.75,Reynolds数取为2×105.通过与相同参数的非偏斜圆柱跨声速绕流对比,分析了偏斜来流对柱体受力和流动特性的影响.由于偏斜来流的流动控制,偏斜圆柱的阻力比非偏斜圆柱的阻力减小高达45%,而振荡力仅受到较小的抑制.偏斜圆柱流场的可压缩性被弱化,激波和小激波消失,而整体流动的模态未改变.偏斜来流使得偏斜圆柱后的剪切层变得更为稳定,进而提升柱体背压.在剪切层的初始发展阶段,剪切层的扰动涡斜脱泻模态和快速动能衰减是偏斜圆柱剪切层更为稳定的两个主要原因.     

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

研究了基于Navier-Stokes方程的脉动速度方程的最优低维动力系统建模理论.最优目标泛函为脉动速度基函数的不可压缩性和正交性.数值计算了充分发展的并排双方柱绕流问题,并基于双尺度全局最优化方法,建立了它的脉动速度的最优动力系统模型.对其相空间轨道、Poincaré截面、分岔特性、功率谱和Lyapunov指数集等动力学特性进行了分析.随着Reynolds数的增加,双方柱绕流的脉动速度方程最优动力系统具有复杂的类倍周期分岔行为.     

Transition of MHD boundary layer flow past a stretching sheet

In this paper a study is carried out to understand the transition effect of boundary layer flow: (1) due to a suddenly imposed magnetic field over a viscous flow past a stretching sheet and (2) due to sudden withdrawal of magnetic field over a viscous flow past a stretching sheet under a magnetic field. In both the cases the sheet stretches linearly along the direction of the fluid flow. Governing equations have been non-dimensionalised and the non-dimensionalised equations have been solved using the implicit finite difference method of Crank–Nicholson type. Comparison between the steady state exact solutions and the steady state computed solutions has been carried out. Graphical representation of the dimensionless horizontal velocity, vertical velocity and local skin friction profiles of the steady state and unsteady state has been presented. Computation has been carried out for various values of the magnetic parameter M. The obtained results has been interpreted and discussed.     

Analysis of viscoelastic fluid flow with temperature dependent properties in plane Couette flow and thin annuli

The steady state flow in very thin annuli has been studied analytically for the case where the annular gap is much smaller than the radius of the inner cylinder and for the outer cylinder rotating at constant angular speed and the inner cylinder at rest. The cylinders were subjected to two different thermal boundary conditions. The exponential effect of temperature on the relaxation time and the viscosity coefficient was accounted into the governing differential equations using Nahme’s law. Effects of viscous dissipation as well as εDe² (viscoelastic index for SPTT constitutive equation) on the dimensionless velocity and temperature profiles have been investigated. Results show that while the properties of the fluid depend on temperature, the velocity and temperature profiles are different compared to those obtained with constant physical properties. The Nahme–Griffith number increases whereas εDe² as a viscoelastic index decreases when temperature dependent physical properties are considered. In addition, the results indicate that the viscous dissipation has a sensible effect on heat transfer and the Nusselt number decreases with an increase in the Nahme–Griffith number.     

Modelling two-dimensional flow past arbitrary cylindrical bodies using boundary element formulations

This paper presents an efficient method of solving Queen's linearized equations for steady plane flow of an incompressible, viscous Newtonian fluid past a cylindrical body of arbitrary cross-section. The numerical solution technique is the well known direct boundary element method. Use of a fundamental solution of Oseen's equations, the ‘Oseenlet’, allows the problem to be reduced to boundary integrals and numerical solution then only requires boundary discretization. The formulation and solution method are validated by computing the net forces acting on a single circular cylinder, two equal but separated circular cylinders and a single elliptic cylinder, and comparing these with other published results. A boundary element representation of the full Navier-Stokes equations is also used to evaluate the drag acting on a single circular cylinder by matching with the numerical Oseen solution in the far field.     

可移动半无限垂直圆柱体温度交变振荡时对MHD自由对流的影响

不可压缩粘性流体,流过可移动、温度交变振荡的半无限垂直圆柱体时,对MHD自由对流影响的数值解进行了研究.应用Crank-Nicolson型的隐式有限差分方法,求解无量纲、不稳定、非线性、耦合的偏微分控制方程.在不同参数下研究速度、温度和浓度分布的变化,还分析了局部及平均的表面摩擦力、Nusselt数和Sherwood数,并以图形形式给出.所得结果与其他文献的结果比较,有着很好的一致性.     

A corrected smoothed particle hydrodynamics method for solving transient viscoelastic fluid flows

In this work, a corrected smoothed particle hydrodynamics (CSPH) method is proposed and extended to the numerical simulation of transient viscoelastic fluid flows due to that its approximation accuracy in solving the Navier–Stokes equations is higher than that of the smoothed particle hydrodynamics (SPH) method, especially near the boundary of the domain. The CSPH approach comes with the idea of combining the SPH approximation for the interior particles with the modified smoothed particle hydrodynamics (MSPH) method for the exterior particles, this is because that the later method has higher accuracy than the SPH method although it also needs more computational cost. In order to show the validity of CSPH method to simulate unsteady viscoelastic flows problems, the planar shear flow problems, including transient Poiseuille, Couette flow and transient combined Poiseuille and Couette flow for the Oldroyd-B fluid are solved and compared with the analytical and SPH results. Subsequently, the general viscoelastic fluid based on the eXtended Pom–Pom (XPP) model is numerically investigated and the viscoelastic free surface phenomena of impacting drop are simulated by the CSPH for its extended application and the purpose of illustrating the ability of the proposed method. The numerical results are presented and compared with available solutions, which shows a very good agreement. All the numerical results show the higher accuracy and better stability of the CSPH than the SPH, especially for larger Weissenberg numbers.     

Expansions at small Reynolds numbers for the flow past a porous circular cylinder

The purpose of this article is to use the method of matched asymptotic expansions (MMAE) in order to study the two-dimensional steady low Reynolds number flow of a viscous incompressible fluid past a porous circular cylinder. We assume that the flow inside the porous body is described by the continuity and Brinkman equations, and the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. Formal expansions for the corresponding stream functions are used. We show that the force exerted by the exterior flow on the porous cylinder admits an asymptotic expansion with respect to low Reynolds numbers, whose terms depend on the characteristics of the porous cylinder. In addition, by considering Darcy's law for the flow inside the porous circular cylinder, an asymptotic formula for the force on the cylinder is obtained. Also, a porous circular cylinder with a rigid core inside is considered with Brinkman equation inside the porous region. Stress jump condition is used at the porous–liquid interface together with the continuity of velocity components and continuity of normal stress. Some particular cases, which refer to the low Reynolds number flow past a solid circular cylinder, have also been investigated.     

Navier-Stokes equation with hereditary viscosity

We rigorously study the Navier-Stokes equation with a hereditary viscous term which depends on the past history. Such models arise in the dynamics of non-Newtonian fluids and also as viscoelastic models for the dynamics of turbulence statistics in Newtonian fluids. This problem is mathematically harder than the conventional Navier-Stokes problem due to the lack of certain global estimates. We prove the local solvability theorem using a suitable intermediate m-accretive quantization of the nonlinear term. Finite speed of propagation property of the vorticity field is also proved.     

Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes

A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A=0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f₀=1.5,2.5,3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discretization of the two-dimensional continuity and unsteady Navier-Stokes equations (when a solid body is present) on a fixed Cartesian grid. Two-fluid model based on improved volume-of-fluid method is used to discretize the free surface interface. The study focuses on the laminar asymmetric flow structure in the near wake region and lock-on phenomena at a Froude number of 0.2 and for the dimensionless cylinder submergence depths, h=0.25, 0.5 and 0.75. The equivorticity patterns and pressure distribution contours are used for the numerical flow visualization. The code validations in special cases show good comparisons with previous numerical results.     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

Variational Inequalities for Navier--Stokes Type Operators and One-Sided Problems for Equations of Viscous Heat-Conducting Fluids

We study a class of stationary variational inequalities for Navier--Stokes type operators that can be used to represent problems with nonlinear boundary conditions for equations of motion of viscous fluids. The main result (the solvability theorem) is used for studying one-sided boundary-value problems for equations of heat convection of viscous fluids.