Cohen区间小波分解及其在边界层探测中的应用

本文利用Cohen等构造的区间小波,在有限区间上进行小波分解,对一类边界问题进行了数值探测,不但求出了问题的数值解,而且进一步确定了边界层的位置。     

超声速钝锥湍流边界层DNS入口边界条件的研究

如何选取恰当的入口条件,是进行湍流边界层直接数值模拟时必须考虑的一个问题.为此建议了一种方法,只需要有平板湍流边界层时间模式直接数值模拟(DNS)所得的一个瞬时的流场,而且其Mach数、Reynolds数及壁面温度条件无需和实际问题中的完全相同,就可导出超声速钝锥湍流边界层空间模式直接数值模拟所需的入口条件.通过3个典型算例,将结果与用其它方法所得结果相比,证实了该方法的可行性.     

转捩边界层中次生流向涡演化的数值研究

采用高精度直接数值模拟方法和高效的特征无反射边界条件,进行可压缩流转捩边界层中出现的次生流向涡演化的数值研究.精细的数值模拟结果清楚地揭示了转捩边界层的复杂流场中次生流向涡的形成和演化过程,探讨它对转捩至关重要的环状涡生成的影响,发现次生流向涡和主流向涡的共同作用形成环状涡的一种新机理.     

抛物化稳定性方程在可压缩边界层中应用的检验

用抛物化稳定性方程（PSE）,研究了可压缩边界层中扰动的演化,并与由直接数值模拟（DNS）所得进行比较．目的在检验PSE方法用于研究可压缩边界层中扰动演化的可靠性．结果显示,无论是亚音速还是超音速边界层,由PSE方法和由DNS方法所得结果都基本一致,而温度比速度吻合得更好．对超音速边界层,还计算了小扰动的中性曲线．与线性稳定性理论（LST）的结果相比,二者的关系和不可压边界层的情况相似．     

可渗透壁面上Falkner-Skan磁流体动力学流动的近似解

研究了可渗透壁面上Falkner-Skan磁流体动力学（MHD）边界层流动问题．利用结合了微分变换法（DTM）和Padé近似的DTM-Padé方法,得到了边界层问题的近似解和壁摩擦因数值．通过建立一个迭代程序,边界层问题的近似解被表示为幂级数的形式,而且以图和表形式对不同参数下的近似解结果与打靶法得到的数值结果进行了对比,近似解和数值解结果高度吻合,从而验证了所得问题近似解和结论的可靠性和有效性．并且,对求得的边界层问题近似解结果进行了讨论,分析了不同物理参数对边界层流动的影响．     

解偏微分方程奇异摄动问题的BL(Boundary Layer)方法

§1 引言 在奇异摄动问题的数值分析中,为了使边界层的典型特性不致丧失,往往需要在边界层的附近将步长变得很小,因而需要相当大的计算工作量。特别对于偏微分方程的奇异摄动问题,由于受计算机条件的限制,有时根本无法获得边界层附近的数值结果。     

求解奇异摄动抛物型对流扩散问题的再生核方法（英文）

基于域分解方法和再生核方法,文章提出了一种求解一维奇异摄动抛物型对流扩散问题的数值方法.原问题被分解成边界层区域问题和正则区域问题,正则区域问题的近似解通过原问题对应的退化问题的解进行近似,边界层区域问题的近似解通过构造合适的再生核,并利用再生核理论给出.三个数值算例的实验结果表明所提出的数值方法是有效的.     

带边界层的线性两点边值问题的打靶——小波配点法

本文将打靶法和小波配点法相结合，提出了打靶－小波配点数值算法，用于求解带边界层的常微分方程边值问题。文中给出了数值算例，并进行了分析，验证了这种方法对处理边界层问题的有效性。     

抛物型方程奇异摄动问题的边界层加权残数法

本文利用奇异摄动问题的边界层特性,结合加权残数法,给出一种边界层问题的处理方法。借助数值计算,得到了抛物型奇异摄动问题的渐近解析解。并证明了解的收敛性和渐近性。     

超音速尖锥边界层中扰动演化特征的数值研究

采用高精度紧致格式, 对超音速尖锥边界层中二维扰动的空间演化, 进行了直接数值模拟．结果表明,虽然尖锥边界层流动存在一定的锥面法向速度,但小扰动的幅值及相位的演化都与由平行流假设得到的线性理论结果吻合．还研究了有限幅值扰动的演化,给出了其演化规律．并在扰动幅值增长到一定值时,发现了小激波．     

反射型激波风洞中激波与边界层的相互作用

本文研究了反射型激波风洞中由于非完全反射对激波与壁面边界层相互作用的影响,给出了在反射激波坐标系中计算边界层速度分布、温度分布和马赫数分布的计算方法.算例表明,在计及氮气的平衡真实气体效应的情形下,随着入射激波马赫数M_s的增大,边界层的最小马赫数从壁面处移到边界层内;随着喷管喉道面积的增大,边界层的最小马赫数、反射激波的分叉角α和分叉区后的射流速度均随之减小.计算结果与实验值相比是一致的.     

Fitted Mesh Method for a Class of Singularly Perturbed Differential-Difference Equations

This paper deals with a more general class of singularly perturbed boundary value problem for a differential-difference equations with small shifts. In particular, the numerical study for the problems where second order derivative is multiplied by a small parameter $ε$ and the shifts depend on the small parameter $ε$ has been considered. The fitted-mesh technique is employed to generate a piecewise-uniform mesh, condensed in the neighborhood of the boundary layer. The cubic B-spline basis functions with fitted-mesh are considered in the procedure which yield a tridiagonal system which can be solved efficiently by using any well-known algorithm. The stability and parameter-uniform convergence analysis of the proposed method have been discussed. The method has been shown to have almost second-order parameter-uniform convergence. The effect of small parameters on the boundary layer has also been discussed. To demonstrate the performance of the proposed scheme, several numerical experiments have been carried out.     

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudo-similarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.     

Segmented Lanczos-Chebyshev reduction method for convection dominated flows

It has been noted repeatedly in computational fluid mechanics literature that upwind-facing “essential” boundary condition poses difficulty for the Galerkin finite element method (and central difference method). Essentially three main remedies have been proposed to correct the spurious “wiggles” which may appear under these circumstances: mesh refinement, alternative numerical formulations, and special boundary layer treatment [1].Here, we seek an alternative formulation which has the same effect as special boundary layer functions based on piecewise polynomial solution via the segmented Lanczos-Chebyshev reduction method.     

超音速边界层中二维扰动的演化及小激波的产生

通过直接数值模拟的方法,对二维超音速边界层中扰动的演化进行了研究．以某一剖面作为入口,加入T-S波,研究小扰动波逐渐增长的演化过程．发现了扰动非线性演化的特征．探讨了二种判断激波存在的方法,证实了超音速边界层中当扰动达到一定的幅值时会有小激波出现．为建立可压缩流稳定性非线性理论提供一定的依据．     

Effects of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over an exponentially stretching surface with suction in the presence of internal heat generation/absorption

In this paper, the problem of unsteady laminar two-dimensional boundary layer flow and heat transfer of an incompressible viscous fluid in the presence of thermal radiation, internal heat generation or absorption, and magnetic field over an exponentially stretching surface subjected to suction with an exponential temperature distribution is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. New numerical method using Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.     

超声速边界层中小幅值T-S波的数值研究

对来流马赫数Ma_∞=45的平板边界层中,幅值A分别为来流速度的0.01,0.001,0.0001倍的扰动波传播的物理过程进行了直接数值模拟。计算采用NND格式。模拟中发现即使扰动幅值尚小时,流场中即已出现小激波。     

A computational method for singularly perturbed nonlinear differential-difference equations with small shift

This paper is devoted to the numerical study of the boundary value problems for nonlinear singularly perturbed differential-difference equations with small delay. Quasilinearization process is used to linearize the nonlinear differential equation. After applying the quasilinearization process to the nonlinear problem, a sequence of linearized problems is obtained. To obtain parameter-uniform convergence, a piecewise-uniform mesh is used, which is dense in the boundary layer region and coarse in the outer region. The parameter-uniform convergence analysis of the method has been discussed. The method has shown to have almost second-order parameter-uniform convergence. The effect of small shift on the boundary layer(s) has also been discussed. To demonstrate the performance of the proposed scheme two examples have been carried out. The maximum absolute errors and uniform rates of convergence have been presented in the form of the tables.     

A Lagrangian simulation of particle deposition in a turbulent boundary layer in the presence of thermophoresis

Knowledge of particle deposition in turbulent flows is often required in engineering situations. Examples include fouling of turbine blades, plate-out in nuclear reactors and soot deposition. Thus it is important for numerical simulations to be able to predict particle deposition. Particle deposition is often principally determined by the forces acting on the particles in the boundary layer. The particle tracking facility in the CFD code uses the eddy lifetime model to simulate turbulent particle dispersion, no specific boundary layer being modelled. The particle tracking code has been modified to include a boundary layer. The non-dimensional yplus, y⁺, distance of the particle from the wall is determined and then values for the fluid velocity, fluctuating fluid velocity and eddy lifetime appropriate for a turbulent boundary layer used. Predictions including the boundary layer have been compared against experimental data for particle deposition in turbulent pipe flow. The results giving much better agreement. Many engineering problems also involve heat transfer and hence temperature gradients. Thermophoresis is a phenomena by which small particles experience a force in the opposite direction to the temperature gradient. Thus particles will tend to deposit on cold walls and be repulsed by hot walls. The effect of thermophoresis on the deposition of particles can be significant. The modifications of the particle tracking facility have been extended to include the effect of thermophoresis. A preliminary test case involving the deposition of particles in a heated pipe has been simulated. Comparison with experimental data from an extensive experimental programme undertaken at ISPRA, known as STORM (Simplified Tests on Resuspension Mechanisms), has been made.     

Numerical Simulation of Pollution Dispersion over Real Terrain

The paper presents a mathematical and numerical investigation of the atmospheric boundary layer (ABL) flow over coal depot. Two mathematical models have been mentioned based upon: 1) the RANS equations in the conservative form and 2) the Boussinesq approximation of RANS equations in the non–conservative form, both formulated for an incompressible flow with a simple algebraic turbulence closure and given stationary boundary conditions. Also pollution dispersion of passive pollutants has been considered.