Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks

A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a ‘universal approximator’ based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of ‘finite element‐type’ discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of , Re = 400 for the driven cavity flow with a density of and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of . Copyright © 2001 John Wiley & Sons, Ltd.     

应用PIV技术测试涡旋波流场

涡旋波流动作为一种特殊的流动现象,可以使流体在相对较宽的槽道中产生较强的波动和对流混合,从而在小Re数条件下起到强化传质的效果。本文利用PIV流场显示技术,对振荡流在非对称槽道中所形成的涡旋波的产生机理和发展规律进行了实验研究和定量分析,测得了涡旋波流场的速度矢量图,阐明了涡旋波流场周期性变化的特点。分析了Re数和St数对涡旋波流动的影响,并得出了旋涡涡心位置以及涡心处涡量的动态变化规律。     

4:1椭球体分离流动湍流特性的试验研究

使用六线涡量探头,对α=30°条件下绕（4:1）椭球体分离流动的湍动能u’2,v’2,w’2,雷诺应力u’v’和涡量Ωx等进行了详尽的测量.应用频谱分析的方法揭示了绕（4:1）椭球体分离流内主附着涡外缘剪切层上的离散小涡的特性.     

Numerical solution of a viscous incompressible flow problem through an orifice

A steady flow problem of a viscous, incompressible fluid through an orifice is widely applicable to many physical phenomena and has been studied previously by many researchers. A problem of such type has been solved by applying LAD method given by Roache [1]. The resulting system of linear equations is solved by Hockney's method [2].     

不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

Existence of Solutions for Three Dimensional Stationary Incompressible Euler Equations with Nonvanishing Vorticity

In this paper, solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary. A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.     

Piecewise analytic bodies in subsonic potential flow

We prove that there are no non-zero uniformly subsonic potential flows around piecewise analytic bodies with three or more protruding corners, assuming the equation of state is a γ-law or other analytic function. This generalizes an earlier result limited to the low-Mach limit for non-degenerate polygons. For incompressible flows we show the velocity cannot be globally bounded.     

2009年一次华北强桑拿天气过程的动力识别

本文数值模拟并诊断分析了2009年7月华北的一次桑拿天过程, 分析了高温高湿天气的环流特征, 温度、 湿度的水平和垂直分布特征, 位涡分布特征等. 分析发现, 此次桑拿天事件高层为反气旋性环流的高压控制, 水平分布图上, 低层相对湿度大. 垂直剖面上, 中低层为下沉气流和暖湿区, 有明显的水汽梯度和垂直温度梯度, 有倾斜的位涡分布. 既然桑拿天发生在夏季普遍高温的大环境之下, 因此靠单纯的温度或湿度来动力识别和诊断桑拿天, 有较大难度. 本文抓住华北地区桑拿天过程高温、 高湿、 高位涡的特点, 引入一个适合于桑拿天的湿热力位涡参数(MTPV, 它表示为▽ q · (▽ θ × ▽ Q), 这里q是湿度, 表示为大气或者云中水汽和所有水凝物的总和, θ 是位温, Q是位涡), 对桑拿天进行动力诊断分析, 并通过实际个例的计算分析作出简化. 个例分析发现, 此次高温高湿的桑拿天过程伴随MTPV的异常. 虽然2009年7月此次华北地区桑拿天过程有较高的温度, 较大的湿度和倾斜位涡发展, 但是单个变量的范围远大于我们要研究的华北地区桑拿天的爆发范围. 而结合这三个变量引入的MTPV及其简化形式, 无论从经向还是纬向剖面图来看, MTPV的异常大值区相对集中在北京及其周边的华北地区对流层的低层, 并维持. 因而, MTPV及其简化形式均能对此次高温高湿的桑拿天进行较好的动力识别。     

内螺纹肋管内流动与传热的数值模拟

本文以空气为介质(Pr=0.698),通过数值模拟的方法在Re=600-2000的范围内对内螺纹肋管内周期性充分发展的层流流动进行了模拟分析,说明了不同Re、螺纹肋的旋转角度α、螺纹肋的牙数N8对速度环量、Nu、Nu和阻力系数的影响,并通过对Nu和速度环量之间的关系进行了分析,得出在内螺纹肋管内强化换热流动中决定换热强度的物理量一速度环量。     

Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties

A shallow water model on a rotating attracting sphere is proposed to describe large-scale motions of the gas in planetary atmospheres and of the liquid in the world ocean. The equations of the model coincide with the equations of gas-dynamic of a polytropic gas in the case of spherical gas motions on the surface of a rotating sphere. The range of applicability of the model is discussed, and the conservation of potential vorticity along the trajectories is proved. The equations of stationary shallow water motions are presented in the form of Bernoulli and potential vorticity integrals, which relate the liquid depth to the stream function. The simplest stationary solutions that describe the equilibrium state differing from the spherically symmetric state and the zonal flows along the parallels are found. It is demonstrated that the stationary equations of the model admit the infinitely dimensional Lie group of equivalence. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 24–36, March–April, 2009.