一类非凸粘性平衡律方程的粘性激波解的存在性与稳定性

本文首先利用几何奇异摄动方法，证明了粘性系数充分小时一类非凸粘性平衡律方程的粘性冲击波的存在性，推广了原来在非线性项严格凸的条件下得到的结果．进而，利用谱分析和上下解方法，证明了对固定的小的粘性系数此类波是全局渐近指数稳定的，推广了反应扩散方程中经典的全局稳定性结果．     

Explicit formulations for evaluation of velocity gradients using boundary‐domain integral equations in 2D and 3D viscous flows

In this paper, explicit boundary‐domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer. Meth. Fluids 2004; 45 :463–484; Int. J. Numer. Meth. Fluids 2005; 47 :19–43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45 :463–484) for 2D and in (Int. J. Numer. Meth. Fluids 2005; 47 :19–43) for 3D problems constitutes a complete boundary‐domain integral equation system for solving full Navier–Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

An unsteady single‐phase level set method for viscous free surface flows

The single‐phase level set method for unsteady viscous free surface flows is presented. In contrast to the standard level set method for incompressible flows, the single‐phase level set method is concerned with the solution of the flow field in the water (or the denser) phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions. A reinitialization procedure has been developed for non‐orthogonal grids with large aspect ratios. A convective extension is used to obtain the velocities at previous time steps for the grid points in air, which allows a good estimation of the total derivatives. The method was applied to three unsteady tests: a plane progressive wave, sloshing in a two‐dimensional tank, and the wave diffraction problem for a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level set method works, as long as the stress on the second phase can be specified (or neglected) and no bubbles appear in the flow during the computation. Copyright © 2006 John Wiley & Sons, Ltd.     

Transonic viscous-inviscid interaction by a finite element method

A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.     

On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions

We establish a connection between the fundamental solutions to some classes of linear nonstationary partial differential equations and the fundamental solutions to other nonstationary equations with fewer variables. In particular, reduction enables us to obtain exact formulas for the fundamental solutions of some spatial nonstationary equations of mathematical physics (for example, the Kadomtsev-Petviashvili equation, the Kelvin-Voigt equation, etc.) from the available fundamental solutions to one-dimensional stationary equations.     

Flows near stagnation points in non-orthogonally colliding disperse viscous flows

Within the framework of a two-fluid dusty-gas model, a family of steady self-similar flows near a stagnation point formed by two different non-orthogonally colliding viscous incompressible streams, one of which contains solid inertial particles, is studied. The limiting case of non-orthogonal impingement of a viscous disperse medium on a rigid wall is considered separately. The possibility of the formation of multiple particle accumulation zones on the envelopes of particle trajectories and on the contact (in the limiting case, rigid) surface is demonstrated. The local structure of the particle velocity and concentration fields is studied. The threshold values of the governing parameters corresponding to qualitative flow pattern reconstruction are found.     

叶轮机械中考虑气体粘性的激波关系

叶轮机械中考虑气体粘性的激波关系黄修乾，徐建中（中国科学院工程热物理研究所北京１０００８０）关键词激波关系，叶轮机械，粘性流动，三维流动１引言随着叶轮机械叶尖速度和负荷的提高，其内部空间激波及激波／边界层相互作用对性能的影响更加显著。就激波／边界层相...     

一类拟抛物粘性扩散方程的整体吸引子

本文考虑出现在人口动力学及稳定分层粘性湍动慢剪切流的热与质量传输理论中一类拟抛物粘性扩散方程解的渐近性态．证明了有限维整体吸引子的存在性．     

VISCOUS FORCES BETWEEN TWO SPHERES COLLIDING THROUGH INTERSTITIAL POWER-LAW FLUID

Interaction between two spheres with an interstitial fluid is essential in Discrete Element modeling for simulating the behaviors of ‘wet‘ particulate materials. In this paper the interaction between two spheres with an interstitial Power-law fluid was approximately resolved as normal and tangential interactive models respectively, for which the governing equations were simplified on the basis of Reynolds approximation. These equations were then solved analytically together with the boundary conditions to obtain the pressure distributions for each individual model, and event ually solutions of the viscous squeeze force and the tangential viscous resistance were obtained, which provide a set of solutions for implementing into DEM code or other purposes.