自由射流不同速度剖面下界面稳定性的伪谱分析

建立了外围为气体,内部为液体射流的双流体模型,并用Chebyshev配点法研究了不同速度剖面自由射流的界面稳定性问题．利用非线性的坐标变换,将物理空间变换到计算空间,得到关于时间频率的广义特征值问题．通过对计算结果的分析与讨论,得出射流稳定性的基本特征及其随各种参数的变化趋势．     

含周期脉动的大密度比气液同轴射流的Floquet稳定性分析

基于周期脉动速度激励下气液同轴射流的数学模型,运用线性稳定性理论,采用Chebyshev配点法和Floquet理论,将含周期脉动分层流的Floquet稳定性分析扩展到大密度比的情况.研究了液铝-氮气射流的参数共振特性,分析了不同的物理参数对系统稳定性的影响,计算了实验工况并和实验结果进行了比较.     

高浓度悬浮固粒对射流界面的粘性稳定性影响

该文首次利用双流体模型和扰动速度势理论,推得含高浓度悬浮固粒的射流界面粘性稳定性方程和对应的固气扰动速度比值方程．通过数值计算,得到了不同雷诺数及固粒属性的射流界面粘性稳定性曲线和对应的固气扰动速度比值曲线．在分析和比较所得的粘性稳定性曲线的基础上,得到了流场雷诺数及固粒特性对射流界面粘性稳定性影响的结论．同时,通过分析所得的固气扰动速度比值曲线,得到了流场雷诺数及固粒等效斯托克斯数对固粒跟随气流的扰动性能的影响的结论．这些结论是首次在计入气流的粘性的条件下得到的,不同于文献［８］和文献［１０］相关的囿于无粘情形的研究,对于两相射流发展的认识和工程实际中实施对两相射流场的人工控制有重要意义．     

含悬浮固粒射流界面稳定性研究

利用气固两相耦合模型,理论推导出含悬浮固粒射流的稳定性方程,通过数值计算得到了两相射流稳定性特征曲线、固气扰动速度比值幅值曲线及固气相位差曲线,进而得到了关于固粒对流场中扰动增长和传播的影响及失稳过程中固粒扰动特性的结论。这些结论对于两相射流发展的认识和工程实际中实施对两相射流场的人工控制有重要意义。     

热传导对气-液射流界面不稳定性的作用机理研究

研究了平面分层气-液射流在非线性温度分布条件下的界面不稳定性性质.考虑了气体的可压缩性、液体的粘性、以及气体热导率和密度随温度变化等事实.并应用正则模态方法将问题转化为四阶变系数常微分方程,用数值积分和多重打靶法对模型的空间模式进行了计算,研究了不稳定模态随各物理参量的变化趋势.计算表明模型所体现的不稳定性特征与其它模型的计算结果是一致的.同时计算还得出气体和液体的温差越小、雷诺数越大、热导率变大均将有利于液体射流有效雾化的结果.该结论与HJE.Co.Inc(Glens Falls,NY,USA)的实验数据是定性吻合的.     

重力对水平Bridgman生长系统中固液界面形状变化的影响

采用有限元方法和自动网格生成技术对水平Bridgman生长系统中的对流效应和相界面形状变化进行了研究 .结果表明 ,强烈的对流使得界面很深地凹向晶相 .在很小Ma数条件下 ,当重力水平大于 1 0 ^-2 g时 ,相界面随重力的增加而急剧扭曲 ;而如果重力小于 1 0^-3 g ,相界面则基本上为一平面 .另一方面 ,即使是在 1 0 ^-6 g的重力水平下 ,不同的生长速率仍然可能对界面形状有很大的影响 .     

圆形垂直浮力射流的稳定性与混合特性研究

建立浅水静止环境中圆形轴对称垂直浮力射流的k-ε模型,采用混合有限分析方法进行了数值计算．针对两种不同的流动形态:近区的混合流体以浮力表面层的形式沿径向扩散的稳定排放;近区产生旋涡,浮力热水对混合热水形成二次挟带的非稳定排放,并对稳定性判据进行了验证,最后对两种不同流动结构下的远区的混合特性进行了数值模拟,结果同Lee和Jirka的试验和理论资料均十分吻合．     

一类双曲方程自由边界问题的稳定性

锅炉炉管中汽水界面的稳定性是一个重要的开问题[1],本文以此问题为模型,讨论了近似带域上双曲方程自由边界问题,利用小参数法和能量不等式,得到了解的渐近稳定性与平均稳定性.所得的稳定性条件,定性地看与工业试验结果相一致.     

利用第二类Chebyshev小波求二阶常微分方程组边值问题的数值解

给出了一个求二阶常微分方程组边值问题数值解的第二类Chebyshev小波配点法.利用第二类Chebyshev小波积分算子矩阵,将问题转化成代数方程组的运算.数值例子说明了方法的准确性及易操作性.另外,为了表明方法的高精度性和有效性,数值算例结果与解析解,以及运用变分迭代法,B样条配点法,连续遗传算法等得到的结果进行了比较.     

微极流体薄膜层通过以滑移速度移动的可渗透无限平板时流体特性变化和热辐射对流动和热传导的影响

微极流体薄膜层通过按滑移速度移动的可渗透无限竖直平板时,研究热辐射对混合对流薄膜层流动和热传导的影响.假定流体粘度和热传导率变化是温度的一个函数.对一些典型的可变参数值,应用Chebyshev谱方法,数值求解流动的控制方程.将所得结果与已发表文献的结果进行比较,结果是一致的.绘出并讨论了可变参数对速度、微旋转速度、温度分布曲线、表面摩擦因数和Nusselt数的影响.     

Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid

Hydrodynamic stability of plane Couette flow of an upper convectedMaxwell fluid is investigated in presence of a transverse magneticfield assuming that the magnetic Prandtl number is sufficientlysmall. The resulting equation is a modified Orr–Sommerfeldequation. The equations of stability are solved numericallyusing Chebyshev collocation method with QZ algorithm. The criticalvalues of Reynolds number, wave number and wave speed are computedand the results are shown through the neutral curves. By increasingthe amount of elasticity to a certain value, it is shown that,as the Hartmann number increases, the minimum critical Reynoldsnumber decreases and it does not increase again in contrastto the Newtonian case.     

A Superconsistent Chebyshev Collocation Method for Second-Order Differential Operators

A standard way to approximate the model problem –u =f, with u(±1)=0, is to collocate the differential equation at the zeros of T _n : x _i , i=1,...,n–1, having denoted by T _n the nth Chebyshev polynomial. We introduce an alternative set of collocation nodes z _i , i=1,...,n–1, which will provide better numerical performances. The approximated solution is still computed at the nodes {x _i }, but the equation is required to be satisfied at the new nodes {z _i }, which are determined by asking an extra degree of consistency in the discretization of the differential operator.     

A Legendre–Galerkin Chebyshev collocation method for the Burgers equation with a random perturbation on boundary condition

In the paper, we apply the generalized polynomial chaos expansion and spectral methods to the Burgers equation with a random perturbation on its left boundary condition. Firstly, the stochastic Galerkin method combined with the Legendre–Galerkin Chebyshev collocation scheme is adopted, which means that the original equation is transformed to the deterministic nonlinear equations by the stochastic Galerkin method and the Legendre–Galerkin Chebyshev collocation scheme is used to deal with the resulting nonlinear equations. Secondly, the stochastic Legendre–Galerkin Chebyshev collocation scheme is developed for solving the stochastic Burgers equation; that is, the stochastic Legendre–Galerkin method is used to discrete the random variable meanwhile the nonlinear term is interpolated through the Chebyshev–Gauss points. Then a set of deterministic linear equations can be obtained, which is in contrast to the other existing methods for the stochastic Burgers equation. The mean square convergence of the former method is analyzed. Numerical experiments are performed to show the effectiveness of our two methods. Both methods provide alternative approaches to deal with the stochastic differential equations with nonlinear terms.     

A Numerical Approach of the sentinel method for distributed parameter systems

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.      

On the stability of the Collocation method for the Radiosity equation on polyhedral domains

This paper investigates the stability of the collocation methodfor the radiosity equation. We introduce graded meshes and trialspaces of piecewise polynomials and prove stability for a modifiedcollocation method. Graded meshes are necessary for higher convergencerates. The generation of triangulations which allow higher-orderapproximations leads to geometrical problems which are interestingin themselves, but do not affect the stability of the collocationmethod.