基于修正并行光滑粒子动力学方法三维变系数瞬态热传导问题的模拟

为了解决传统光滑粒子动力学(SPH)方法求解三维变系数瞬态热传导方程时出现的精度低、稳定性差和计算效率低的问题,本文首先基于Taylor展开思想拓展一阶对称SPH方法到三维热传导问题的模拟,其次引入稳定化处理的迎风思想,最后基于相邻粒子标记和MPI并行技术,结合边界处理方法得到一种能够准确、高效地求解三维变系数瞬态热传导问题的修正并行SPH方法.通过对带有Direclet和Newmann边界条件的常/变系数三维热传导方程进行模拟,并与解析解进行对比,对提出的方法的精度、收敛性及计算效率进行了分析;随后,运用提出的修正并行SPH方法对三维功能梯度材料中温度变化进行了模拟预测,并与其他数值结果做对比,准确地展现了功能梯度材料中温度变化过程.     

基于SPH方法的瞬态粘弹性流体的数值模拟

运用SPH(Smoothed Particle Hydrodynamics)方法模拟基于Oldroyd-B模型的平面突然起动Couette流,通过数值解与解析解的比较,验证SPH方法模拟瞬态粘弹性流动的准确性;且对基于Oldroyd-B模型的方腔驱动流进行SPH模拟.采用一种新的固壁边界处理方法,有效地防止了粒子穿透,提高数值计算的准确性.用数值算例验证SPH方法对粘弹性流体模拟的有效性和稳定性.     

瞬态热传导问题的一种单纯边界元算法

给出了一种二维瞬态热传导问题的单纯边界元算法，它完全在边界上离散数值求解，通过数值算例验证表明该方法充分体现了边界元法的独特优点。     

瞬态热传导问题的复变量重构核粒子法

在重构核粒子法的基础上,引入复变量,讨论了复变量重构核粒子法.复变量重构核粒子法的优点是在构造形函数时采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于瞬态热传导问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,采用罚函数法引入本质边界条件,建立了瞬态热传导问题的复变量重构核粒子法,推导了相应的计算公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、精度高的优点.最后通过数值算例证明了该方法的有效性. 关键词： 重构核粒子法 复变量重构核粒子法 修正函数 瞬态热传导问题     

变系数瞬态热传导问题边界元格式的特征正交分解降阶方法

提出了一种基于边界元法求解变系数瞬态热传导问题的特征正交分解(POD)降阶方法,重组并推导出变系数瞬态热传导问题适合降阶的边界元离散积分方程,建立了变系数瞬态热传导问题边界元格式的POD降阶模型,并用常数边界条件下建立的瞬态热传导问题的POD降阶模态,对光滑时变边界条件瞬态热传导问题进行降阶分析.首先,对一个变系数瞬态热传导问题,建立其边界域积分方程,并将域积分转换成边界积分;其次,离散并重组积分方程,获得可用于降阶分析的矩阵形式的时间微分方程组;最后,用POD模态矩阵对该时间微分方程组进行降阶处理,建立降阶模型并对其求解.数值算例验证了本文方法的正确性和有效性.研究表明:1)常数边界条件下建立的低阶POD模态矩阵,能够用来准确预测复杂光滑时变边界条件下的温度场结果;2)低阶模型的建立,解决了边界元法中采用时间差分推进技术求解大型时间微分方程组时求解速度慢、算法稳定性差的问题.     

光滑粒子动力学SPH方法应力不稳定性的一种改进方案

光滑粒子动力学方法是一种拉格朗日型无网格粒子方法,在模拟大变形和自由表面流方面具有特殊的优势,已经在工程和科学领域得到了广泛的应用．然而,长期以来,传统光滑粒子动力学方法一直受到应力不稳定性的困扰,从而限制了它的进一步发展和应用．应力不稳定性的根本原因在于应力状态与核函数的不匹配：负压状态下粒子间产生吸引力,吸引力随着粒子间距的减小而增大,导致拉伸不稳定性;正压状态下粒子间产生排斥力,排斥力随着粒子间距的减小而先增大后减小,导致压缩不稳定性．本文通过改进光滑粒子动力学方法的核函数和离散格式,使得无论在正压还是负压状态下粒子间的作用力恒为排斥力,且排斥力随着粒子间距的减小而增大,从而防止粒子聚集等现象,解决应力不稳定问题．分别使用改进前后的光滑粒子动力学方法模拟两个典型的应力不稳定算例,结果表明本文的改进方法能够有效地消除应力不稳定性．     

基于改进布谷鸟算法识别瞬态热传导问题的导热系数

基于改进布谷鸟算法反演瞬态热传导问题随温度变化的导热系数.采用Kirchhoff变换将非线性热传导问题转换为线性热传导问题,使用边界元法求解瞬态热传导正问题.将导热系数的反演转化为函数表达式中未知参数的反演,使用改进布谷鸟算法求解未知参数.与共轭梯度法相比,改进布谷鸟算法对迭代初值不敏感;与布谷鸟算法相比,改进布谷鸟算法迭代次数大大减少.数值算例表明对改进布谷鸟算法,增加测点数量迭代次数增加;增加鸟巢数量迭代次数减少;减小测量误差计算结果更精确,同时迭代次数更少.数值算例验证了改进布谷鸟算法反演导热系数的准确性和有效性.     

多孔介质中流体输运的孔尺度SPH模拟

本文采用光滑粒子流体动力学(SPH)方法[1]对流体流过多孔介质的过程进行数值模拟,方法与程序用经典的Poiseuille流与多孔介质流动的Kozeny解进行了验证.PH进一步用于数值模拟跨膜流动,获得了跨膜流动中速度场随时间的演化过程.多孔膜孔径在1 靘到200 靘范围内,流体跨膜渗透速度的SPH结果与K-K方程的计算值吻合较好.文中还讨论了粒子数目与计算精度的关系.本文的计算结果表明SPH方法具有模拟多孔介质微流动的能力.     

大平板瞬态热传导问题的一种新的近似解法

１引言大平板瞬态热传导问题有着广泛的工程应用背景。对于复杂的初边值条件或含内热源问题,以及工程上常见的多层复合平壁对象,分析求解难度很大甚至无法求解。在此类情况下往往采用数值方法。但是单纯的数值解不便于理解影响该问题的各种参数的物理意义。因此,各种近似分析方法得到了发展［１,２］。但在近似精度上,往往难以对整个时间坐标范围都达到较高的精度,这就使得近似解更多地局限于定性分析。此外,对于不同的初边值条件或含内热源问题,近似解的形式相异,降低了解的通用性。增加了求解的工作量。本文提出一种基于矩阵理论…     

高速碰撞SPH方法模拟中的初始光滑长度和粒子间距

采用光滑粒子流体动力学方法对高速碰撞问题作数值模拟,分析初始光滑长度和非一致粒子间距对计算结果的影响,提出修正光滑长度法,并引入XSPH速度纠错公式.数值结果表明,初始光滑长度越大,弹丸的刚性越小,h₀的合理取值范围应为d₀<h₀≤1.5d₀;粒子间距越小,材料的刚性越小.非一致粒子间距和均匀粒子分布的计算结果吻合的较好.     

A new complex variable meshless method for transient heat conduction problems

<正>In this paper,based on the improved complex variable moving least-square(ICVMLS) approximation,a new complex variable meshless method(CVMM) for two-dimensional(2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations,and the essential boundary conditions are imposed by the penalty method.As the transient heat conduction problems are related to time,the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization.Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained.In order to demonstrate the applicability of the proposed method,numerical examples are given to show the high convergence rate,good accuracy,and high efficiency of the CVMM presented in this paper.     

A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.     

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

In this paper, the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.     

An improved local radial point interpolation method for transient heat conduction analysis

The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method （FEM） as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline （TPS） radial basis functions.     

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.     

The improved element-free Galerkin method for three-dimensional transient heat conduction problems

With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.     

Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson’s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.