线性与非线性波的Chebyshev广义有限谱模拟

给出求解二维线性与非线性波的Chebyshev广义有限谱模拟方法.结合时间层次的高精度预报-校正方法，模拟了二维线性浅水驻波和波在浅滩的非线性变形.方法能够准确模拟水波的物理特征. 关键词： Chebyshev广义有限谱 线性波 非线性波     

GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

A generalized finite spectral method is proposed. The method is of high-order accuracy. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Her-mite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.     

求解温盐双扩散系统的一种高精度方法

引入边界拟合坐标系来研究温盐双扩散系统。为了提高求解的精确性 ,对流项采用四阶精度的迎风格式 ,扩散项和涡量方程的浮力项则采用四阶精度的中心差 ,因此本文的方法是高精度的方法。首先针对温度占优( Rρ=0 .32 )和盐度占优 ( Rρ=1 .6 8)的情形进行了验证性计算 ,得到了与前人一致的结果。进一步 ,本文系统给出了不同的盐度通量强度下的流动形态 ,包括对称结构 ,不对称结构 ,反转结构等 ,结果与前人的吻合。     

多孔介质中盐指现象的数值模拟

运用基于杂交网格的高精度数值方法研究了多孔介质中的盐指现象.该算法将基于边界拟合坐标下的高精度有限差分法和高精度的泊松方程快速求解器有效地结合在一起,从而达到提高整体的计算精度、计算效率和稳定性的目的.通过比较不同孔隙率的多孔介质对盐指对流的传热传质效应的影响,发现在标准孔隙率较低的多孔介质中,盐度扩散的速度明显比热扩散的速度快,盐指很快触及上下壁面,使得上下层的盐度梯度迅速减小,这是与非多孔介质具有明显差异之处. 关键词： 多孔介质 双扩散对流 盐指     

稳定性分析数值方法综述

本文综述了流体动力学稳定性分析中所使用过的数值方法,每种方法都通过文献中举出的一个典型例子作了说明。努力了解近代稳定性计算中所采用的各种数值方法,并汇总在附录Ⅱ中。对与无粘问题有关的各种困难作了解释。还讨论了Navier-Stokes方程作为初值问题的直接解法。      

扩展型动网格的Chebyshev有限谱方法

给出了基于非均匀网格的Chebyshev有限谱方法．提出了可生成两种类型扩展型动网格的均布格式．一种类型的网格被用来提高波面附近的分辨率,另一种类型则用在梯度较大的流动区域．由于采用Chebyshev多项式作为基函数,该方法具有高阶精度．从上个时间步到当前时间步,两套不均匀网格间的物理量采用Chebyshev多项式插值．为使方法在时间离散方面保持高精度,采用了Adams-Bashforth预报格式和Adams-Moulton校正格式．为了避免由Korteweg-deVries(KdV)方程的弥散项引起的数值振荡,给出了一种非均匀网格下的数值稳定器．给出的方法与具有分析解的Burgers方程的非线性对流扩散问题和KdV方程的单孤独波和双孤独波传播问题进行了比较,结果非常吻合．     

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.     

一维Burgers方程和KdV方程的广义有限谱方法

给出了高精度的广义有限谱方法．为使方法在时间离散方面保持高精度,采用了Adams-Bashforth 预报格式和Adams-Moulton校正格式,为了避免由Korteweg-de Vries(KdV)方程的弥散项引起的数值振荡, 给出了两种数值稳定器．以Legendre多项式、Chebyshev多项式和Hermite多项式为基函数作为例子,给出的方法与具有分析解的Burgers方程的非线性对流扩散问题和KdV方程的单孤独波和双孤独波传播问题进行了比较,结果非常吻合．     

Numerical Simulation for thermohaline multiple equilibrant system in non—rectangular domains

In this paper, incompressible, double-diffusive convection is simulated using finite-difference schemes. The Navier--Stokes equations are expressed in terms of stream function and vorticity. Because of the existence of large velocity, temperature and salinity gradients in boundary layers, a boundary-fitted coordinate system is used to concentrate the grid points near the wall and fit complex boundaries. The finite-difference methods used include the high-order accurate upwind difference scheme. It is shown that the scheme is a good candidate for direct simulations of double-diffusive convection flows. The proposed method is first applied to symmetry breaking and overturning states in thermohaline-driven flows in trapezoid basins. The basic phenomena agree well with those by Dijkstra and Molemaker (1997 {\em J. Fluid Mech.} {\bf 331} 169) and Quon and Ghil (1992 {\em J. Fluid Mech.} {\bf 245} 449), but symmetry breaking and overturning states can occur in an asymmetric geometrical region without perturbations. Then the method is applied to double-diffusive convections in a cavity with opposing horizontal temperature and concentration gradients at large thermal ($Rt$), solutal ($Rs$) Rayleigh numbers and Lewis number. There are three straight sides and a sine curve side in the cavity. Basically, numerical results are in agreement with those of Lee and Hyun (1990 {\em Int. J. Heat Mass Transfer} {\bf 33} 1619) qualitatively, but eddies mixing in the top left-hand corner near the curved wall affects the layered structure.     

群沙射流结构的实验研究

本文以90－150μm的标准细沙为研究对象，利用超声波速度剖面测量仪和数码摄录机进行了垂直入水群沙射流的实验研究，给出了的群沙入水后的运动规律。我们发现，群沙湍射入水的一霎那，底部瞬时产生反射波，由它带动的流速与群沙入水带动的流速同量级。