流体晃动时域双协边界元法分析

利用双协边界元法在时域内对流体晃动问题进行分析,推导出边界积分方程及相应的边界条件。分析过程中考虑流体的粘性,自由面上的动力学条件为法向正应力和切向剪应力为零。固壁面上采用流体质点与固壁质点速度相等的条件。时域的离散采用差分法,并利用时间步迭代,逐步追踪流体自由面,在流体的不断变动的边界上考虑其边界条件。数值结果表明本文的双协边界元法是可行的。     

高速冲击过程数值分析的再生核质点法

利用新型的无网格方法-再生核质点方法对高速冲击过程进行数值模拟，给出了控制 方程，分析中引入Bordner-Partom本构模型来实现材料高速冲击条件下的大应变和高应变 率的特性，提出了新的接触面处理方法，介绍了速度配点法来实现接触面及其它本质边界的 速度条件. 数值模拟表明，再生核质点法能够准确模拟高速冲击过程，具有较高的计算精度.     

液体调谐减振器的分析

本文利用Ｌａｍｂ变换，考虑液体的粘性，略去二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程中的非线性预后，建立了频域内Ｎａｖｉｅｒ－Ｓｔｏｋｒｅｓ方程的边界积分表达式，完整地处理了边界条件（包括自由面边界条件和固壁边界条件）并且给出了液体随结构振动时的附加质量与阻尼的计算表达式。     

弹性波混合差分解法的透射边界条件

文中将基于离散应力、速度混合变量弹性波方程的各种数值解法统称为混合差分法，该文研究这类解法中人工边界的透射边界条件。基于波动沿边界法向传播的特征量分析，给出了横观各向同性介质中复杂形状边界的透射条件。该文是一种局部透射条件，所需计算量极小。文中将此方法与交错网格差分解法结合并应用于横观各向同性介质弹性波计算。数值算例及反射系数分析表明，该方法很好地消除了人工边界对来波的反射。     

透射边界高频失稳机理及其消除方法——SH波动

用有限元法求解近场波动问题,须选取人工边界条件以实现对无限域稳定、高效的数值模拟. 该文探讨了SH波导 有限元数值模拟中透射边界引发的高频失稳问题. 从离散模型出发,分析了内节点与人工边界节点运动方程频散曲线之间的匹配关系,揭示了高频失稳的一种机理,即二者相互耦合所 得计算方案支持自发从人工边界向计算区域内行进的高频波动. 提出通过调整内节点运动方程以改变这一匹配关系,从而消除失稳的措施. 理论分析与数值结果表明该措施能有效地消除高频振荡失稳.     

重力作用下液体自由面的数值解

给出一种重力作用下静止液体自由面的数值解方法。根据流体力学Young-Laplace公式和微分几何学主曲率方程,并利用液体自由面的对称性质,导出重力作用下静止液体自由面母线的常微分控制方程。为了使该方程便于利用现有的Runge-Kutta法,根据问题的物理背景,将体积边界条件转化为固-液接触面半径条件;采用一种坐标变换,避免了该方程数值计算中刚性问题的出现。最后给出了算例。     

直接边界元法三维自由面兴波时域模拟

应用直接边界元法在时域中求解稳定航速运动的三维自由面兴波问题.基于格林定理,在所有边界面上划分网格,对边界积分方程进行数值离散,采用线性自由面边界条件,随时间步进更新自由面势.由于物体空间位置移动辐射条件不需要单独表述,迭代过程中自由面计算域保持不变.以割划水面NACA0024为例,计算模拟了自由面兴波稳定波形;提出了求解矩阵方程组奇异性的处理方法和解决割划问题的动网格技术.本文计算结果和有限体积法及有关试验结果对比表明,该方法是可靠的.     

集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。     

R-函数理论及准Green函数方法在正交各向异性板振动问题中的应用

首次将R-函数理论及准Green函数方法应用于求解固支正交各向异性薄板的自由振动问题。首先引入参数变换,将正交各向异性薄板的自由振动微分方程转化为双调和算子的边值问题,并应用R-函数理论,以解析函数形式描述复杂边界形状;利用问题的基本解和边界方程构造了一个准Green函数,该函数满足了问题的齐次边界条件;通过R-函数理论构造适当的边界方程,消除了积分方程核的奇异性;再采用Green公式将其化为第二类Fredholm积分方程。数值算例表明:该方法减少了理论计算量,精度较高。本文还证明了其优越性和正确性,是一种新型的数学方法。     

非线性侵彻动力过程的再生核质点法

通过在再生核质点法中引入Johnson-Cook本构方程及损伤模型,并利用新型的滑移面算法及配 点法解决再生核质点法中的接触面和质点滑移问题,方便实现边界条件和计算过程中质点速度调整。通过侵 彻过程再生核质点法研究,实现了弹丸侵彻靶板过程的模拟分析,避免了有限元法中单元严重变形和破坏过 程的网格重构困难,提高了分析精度和计算速度,可方便模拟侵彻的大变形和高应变率现象。     

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.     

A boundary element method for small-amplitude viscous fluid sloshing in couple with structural vibration

A boundary element method is presented for the coupled motion analysis of structural vibration with small-amplitude fluid sloshing in two-dimensional space. The linearized Navier-Stokes equations are considered in frequency domain and transformed into boundary integral equations. An appropriate fundamental solution for the Helmholtz equation with pure imaginary constant is found. The condition of zero-stress is imposed on the free surface, and non-slip condition of fluid particles is imposed on the walls of the container. For rigid motion models, the expressions for added mass and added damping to the structural motion equations are obtained. Some typical numerical examples are presented.     

Effects of partial slip on chemically reactive solute transfer in the boundary layer flow over an exponentially stretching sheet with suction/blowing

The boundary layer flow and mass transfer toward an exponentially stretching porous sheet are analyzed in this paper. Velocity slip is considered instead of the no-slip condition on the boundary. Self-similar equations are obtained by using similarity transformations. Numerical solutions of these equations are obtained by the shooting method. It is found that the fluid velocity and concentration decrease with increasing slip parameter. The fluid velocity decreases with increasing suction parameter.     

Viscoelastic MHD flow boundary layer over a stretching surface with viscous and ohmic dissipations

In this study the momentum and heat transfer characteristics in an incompressible electrically conducting viscoelastic boundary layer fluid flow over a linear stretching sheet are considered. Highly non-linear momentum and thermal boundary layer equations are reduced to set of nonlinear ordinary differential equations by appropriate transformation.     

Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink

The boundary layer flow and heat transfer of a fluid through a porous medium towards a stretching sheet in presence of heat generation or absorption is considered in this analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. These transformations are used to convert the partial differential equations corresponding to the momentum and the energy equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity decreases with increasing temperature-dependent fluid viscosity parameter up to the crossing-over point but increases after that point and the temperature decreases in this case. With the increase of permeability parameter of the porous medium the fluid velocity decreases but the temperature increases at a particular point of the sheet. Effects of Prandtl number on the velocity boundary layer and on the thermal boundary layer are studied and plotted.     

浸入边界法及其应用

浸入边界法主要用于模拟存在复杂外形结构的流场的运动情况和处理各种动边界问题,目前已广泛应用于计算流体力学领域.浸入边界法既是数学建模方法又是数值离散方法,它将物体边界与流体的相互作用通过在流体运动方程中加体积力项来体现,并在数值计算中采用简单的笛卡尔网格,避免了按照物体边界形状生成贴体网格时所遇到的各种问题.浸入边界法分为连续力法和离散力法:连续力法主要用于处理弹性边界问题,它的力源项满足特定的力学关系式;离散力法主要用于处理固体界面问题,它的力源项由边界条件推导得到.着重阐述了浸入边界法的基本原理和数学构造,对目前已有的几种不同的浸入边界法做了简单地介绍,并给出了一些应用实例,最后提出了浸入边界法未来的发展方向.     

Existence of Strong Solutions for a System Coupling the Navier–Stokes Equations and a Damped Wave Equation

We consider a fluid–structure interaction problem coupling the Navier–Stokes equations with a damped wave equation which describes the displacement of a part of the boundary of the fluid domain. The system is considered first in the two-dimensional setting and in a second part it is adapted to the three-dimensional setting.     

MHD forced convection boundary layer flow with a flat plate and porous substrate

The flow and heat transfer for an electrically conducting fluid with a porous substrate and a flat plate under the influence of magnetic field is considered. The magnetic field is assumed to be uniform and also along normal to the surface. The momentum and energy equations are transformed to ordinary differential equations by using suitable similarity transformation and are solved by standard techniques. But the energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. Numerical results are presented through graphs with various values of magnetic parameter for both velocity and thermal boundary layers along with Nusselt number and for various values of Prandtl number and Eckert number in thermal boundary layer.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.     

Uniqueness theorems in the theory of thermoelasticity for solids with double porosity

In this paper the coupled linear theory of thermoelasticity for solids with double porosity is considered. The governing system of field equations of this theory is based on motion equations, conservation of fluid mass, constitutive equations, extended Darcy’s law for materials with double porosity and Fourier’s law for heat conduction. A wide class of the basic internal and external boundary value problems (BVPs) of steady vibrations is formulated and uniqueness theorems for regular (classical) solutions of these BVPs are proved.