不可压缩流动的移动粒子半隐式法数值模拟

介绍了一种新的移动粒子半隐式方法。该方法采用Lagrange描述,用一系列离散粒子代替流体,通过半隐式求解和时间推进法来进行计算,弥补了传统网格法对复杂形状、大变形、高速撞击等情况下网格划分和重构过于繁琐的缺点,在模拟不可压缩流动问题中得到了较好的效果。     

Simulation of the Action of a Permeable Barrier on an Ideal Incompressible Channel Flow

Plane ideal incompressible flow in a rectangular channel partitioned by a thin permeable barrier (lattice) is considered. In flowing through the lattice the stream suddenly (jumpwise) changes direction and loses energy. The flow is assumed to be vortical; the vorticity is discontinuous on the lattice. A mathematical formulation of the problem for the stream function is proposed in the form of a nonlinear elliptic equation with coefficients discontinuous on the lattice line. A numerical solution is constructed using the finite-element iteration method. The results of the numerical simulation show how the flow velocity profile in the channel can be controlled by means of permeable barriers.     

不可压气流中二元机翼的分叉分析

本文分析了不可压气流中带有非线性俯仰刚度二元机翼的分叉问题.分析采用了工程实用的等效线化法和作为比较标准的数值积分法,并借助计算机代数系统按Hassard渐近展开算法及平均化算法求得解析解进行比较.从而论证等效线化法的可用性.     

Direct Numerical Simulation of the Three-Dimensional Transition to Turbulence in the Incompressible Flow around a Wing

The onset of the secondary instability and the successive steps ofthe 3D transition to turbulence are examined in the flow around a wing of NACA0012 section, constant along the spanwise direction. The wing is placed in a uniform flow upstream, at 20° of incidence and at the Reynolds number of 800. The spanwise length is equal to four chords. The objectives of this study are the identification of the three-dimensional transition mechanism and the development of the early stages of turbulence in the present class of unsteady aerodynamic flows. A detailed processing of the DNS signals carried out by an appropriate conditional sampling allows the identification of the physical mechanisms related to the birth of turbulence and to the non-linear interaction with the 3D coherent structures in the near region.     

A Model of Discontinuous, Incompressible Two-Phase Flow

Lack of hyperbolicity is a recurring problem for models of two-phase flow assuming the form of systems of balance laws. In particular, smooth solutions occur only for very special initial data, and the standard results on the local structure of discontinuous weak solutions do not apply to such nonhyperbolic systems. A simple example is inviscid, incompressible two-fluid flow with a single pressure. We suggest that such an unattractive mathematical feature may result from the mathematical derivation of the model, rather than from the underlying physical assumptions. In particular, for the case described above we present an alternative treatment which leads to a consistent model for piecewise smooth, discontinuous solutions. We obtain admissibility conditions for the anticipated discontinuities by considering the limit of vanishing viscosity with a convenient dissipation term.      

不可压缩流中机翼颤振稳定性研究

研究两个自由度的机翼在不可压缩流作用下颤振的分支问题.运用罗司-霍维茨判据确定系统的分叉点,应用中心流形理论将四维系统降为二维系统,用直接求周期解方法对分叉点的真假中心及稳定性问题进行了分析,并研究了系统的极限环颤振.结果表明,本文研究的分叉点不是中心,而是稳定或不稳定焦点.在两个分叉点处,系统发生了超临界和亚临界Hopf分叉,产生稳定或不稳定极限环.     

粘性不可压缩流体定常层流管流及柱体的扭转

本文用加权残数法求得了任意等腰三角形及矩形截面的柱体的扭转问题以及和柱体形状相同的等截面长管的不可压缩粘性流体的定常层流问题的近似解.近似解有较高的精确度.另外,文中还提出了变率配域法的概念.     

Incompressible Polymer Fluid Flow Past a Flat Wedge

A problem of an incompressible polymer fluid flow past an infinite flat wedge is considered. The flow moves parallel to the plane of symmetry of the wedge and normal to the wedge rib. It is demonstrated that two surfaces of strong discontinuities are needed for the no-slip condition to be satisfied on the wedge surface. Steady solutions of the problem are studied, and the flow is shown to be asymmetric with respect to the plane of symmetry of the wedge.     

Incompressible Limit for the Compressible Flow of Liquid Crystals

The connection between the compressible flow of liquid crystals with low Mach number and the incompressible flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the compressible flow of liquid crystals to the weak solutions of the incompressible flow of liquid crystals is proved when the Mach number approaches zero; that is, the incompressible limit is justified for weak solutions in a bounded domain.     

Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.      

Hopf Bifurcation in Viscous Incompressible Flow Down an Inclined Plane

We provide the Hopf bifurcation theorem, which guarantees the existence of time periodic solution bifurcating from the stationary flow down an inclined plane under certain assumptions on the eigenvalues of the problem obtained by linearization around the stationary flow. Since we reduce the problem to the fixed domain, the inhomogeneous terms of reduced equations and reduced boundary conditions contain the highest derivatives. To deal with these we apply the Lyapunov–Schmidt decomposition directly.     

Higher-Order Flux-Limiting Schemes for the Finite Volume Computation of Incompressible Flow

Numerical modelling of convection suitable for cell-centred finite volume methods for incompressible flow is considered. Higher-order accurate and oscillation-free solutions are obtained through flux limiting, Two improvements are discussed: the enhancement of accuracy at smooth extrema of the TVD solution, and the construction of flux limiters, which is based on polynomial interpolants in the normalized variable space. Some implementation issues are outlined. Numerical examples are provided to illustrate these advancements.     

A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems

This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier–Stokes–Oseen flow, the Navier–Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein–Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.     

The Local Analysis of Changing Force Balances in Immiscible Incompressible Two-Phase Flow

The balance of viscous, capillary and gravity forces strongly affects two-phase flow through porous media and can therefore influence the choice of appropriate methods for numerical simulation and upscaling. A strict separation of the effects of these various forces is not possible due to the nature of the nonlinear coupling between the various terms in the transport equations. However, approximate prediction of this force balance is often made by calculation of dimensionless quantities such as capillary and gravity numbers. We present an improved method for the numerical analysis of simulations which recognises the changing balance of forces – in both space and time – in a given domain. The classical two-phase transport equations for immiscible incompressible flow are expressed in two forms: (i) the convection–diffusion-gravity (CDG) formulation where convection and diffusion represent viscous and capillary effects, respectively, (ii) the oil pressure formulation where the viscous effects are attributed to the product of mobility difference and the oil pressure gradient. Each formulation provides a different perspective on the balance of forces although the two forms are equivalent. By discretising the different formulations, the effect of each force on the rate of change of water saturation can be calculated for each cell, and this can be analysed visually using a ternary force diagram. The methods have been applied to several simple models, and the results are presented here. When model parameters are varied to determine sensitivity of the estimators for the balance of forces, the CDG formulation agrees qualitatively with what is expected from physical intuition. However, the oil pressure formulation is dominated by the steady-state solution and cannot be used accurately. In addition to providing a physical method of visualising the relative magnitudes of the viscous, gravity and capillary forces, the local force balance may be used to guide our choice of upscaling method.     

分块隐式有限差分法计算弯管紊流

本文利用贴体坐标系中分块隐式有限差分法计算矩形截面90°弯管中不可压恒定紊流.在计算中,雷诺方程的数值离散采用混合差分格式,局部联立求解雷诺方程和连续方程而得到速度压力解.在全流场的迭求解过程中采用对称联立Gauss—Seidel法.利用标准K-ε紊流模型模拟紊流.计算结果与有关试验进行了对比.     

一种可压缩与不可压缩气体流动的统一算法及其应用

本文采用伪时间变化率项及其"预处理"矩阵,并结合LU-SGS离散格式,发展了可压缩与不可压缩气体流动求解的统一算法.该方法有效地消除了采用可压缩方法求解低速流动时容易产生的"刚性"问题,减小了由于压力项在低速情况下产生的舍入误差.同时,在求解低速与高速并存的流场流动时,无需进行预处理矩阵的转换,实现了可压缩与不可压缩气体流动的统一理论求解.作为算法有效性的验证,本文分别计算了低速、高速、高低速混合流动的典型算例.计算值的验证结果比较表明,对求解马赫数大范围变化情况下的流场,具有很好的收敛性与稳定性,而且收敛速度基本不受流动速度的影响.这个算法程序为今后发展用于燃烧反应流动和密度梯度驱动流动的分析建立了方法基础.     

Finite Element Error Analysis Approach for Three-Dimensional Incompressible Viscous Fluid Flow Analysis

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the analyses of convection-diffusion problems and two-dimensional viscous fluid flow problems. In this modified Galerkin method, the inertia term is considered explicitly, so only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, we proposed a new finite element formulation for three-dimensional incompressible viscous fluid flow analysis. This formulation (‘MS’ algorithm and ‘MSR’ algorithm) is based on the modified Galerkin method coupled with the Semi-Implicit Method for Pressure-Linked Equations. The cubic cavity flow problems were investigated for the Reynolds number of 400, 1,000, 2,000 and 3,200 using non-uniform meshes. Finally, we confirmed the effectiveness of our proposed method through the comparison with other research works.     

Unsteady Self-Similar Flow of a Viscous Incompressible Fluid in a Plane Divergent Channel

The problem of two-dimensional unsteady flow of a viscous incompressible fluid in a sector-like domain is considered. Initially a strictly radial flow is imposed, which makes it possible to seek solutions within the class of self-similar flows. A numerical method based on mixed finite-difference and spectral spatial discretization is developed, making it possible to find the self-similar solution efficiently. The process of development and establishment of the steady Hamel-Jeffery and Moffatt flows is modeled mathematically.     

非稳态不可压缩自由表面粘性流体的三维数值计算

扩展了相对体积算法，计算了变速旋转的敞口圆筒内水的真实非稳态流动。采用了原始变量、交错非等分网格和显式迭代。计算结果与实验现象相吻合。当圆筒长时间等速旋转，其内流体与筒体一起作刚性旋转时，计算自由表面形状与流体力学理论公式的预言吻合得很好。