考虑液滴尺寸分布气液两相爆轰流场数值仿真

研究脉冲爆轰发动机喷射装置模型问题,针对两相爆轰流场中燃料液滴半径实际上分布的不均匀性,为了建立更符合实际的模型,提出了多尺寸分布的两相爆轰方程.应用二维守恒元和求解元方法(CE/SE方法)对其进行数值仿真,得到了液滴初始半径分布对管内流场的影响.液滴初始半径分组时爆轰波速度介于不分组时最小液滴半径和最大液滴半径的计算值之间;分析了液滴初始半径不同分组时,液滴平均半径越小,爆轰波最大压力和爆轰波出口速度越大.仿真结果证明用CE/SE方法可有效捕获两相爆轰波间断能力.研究成果为脉冲爆轰发动机喷射雾化装置设计提供设计依据.     

基于Potts模型的图像分割快速算法

Potts模型是一种通用的多相图像分割的变分模型,其极值问题需要迭代求解一系列偏微分方程。针对其求解过程计算效率较低的问题,提出一种基于对偶方法的快速算法。采用离散二值标记函数作为特征函数,利用Lagrange乘子法把对特征函数的约束加入能量泛函,然后引入对偶变量改写模型中的长度项,利用KKT的条件得到特征函数的二值解以及对偶变量的简单迭代格式。通过数值实验将该方法与梯度降方法、对偶方法和Split Bregman方法进行比较。实验结果表明,该算法的计算效率和分割准确性都高于其他三种方法。     

二相湍流爆轰流场的数值仿真

研究脉冲轰发动机效率优化设计问题,由于湍流对两相爆轰流场有较大影响,要求明确两相爆轰流场的特点.为了进一步明确上述问题,提出建立轴对称两相爆轰低雷诺数湍流模型,应用求解元与守恒元方法(简称CE/SE方法)进行数值仿真.仿真结果表明,湍动能随着爆轰波的传播而前进,且湍动能值在管子的中心部位较大.明确气相轴向速度在爆轰波阵面上比径向速度大的特点.仿真也为爆轰湍流流场效能的认识和提高脉冲发动机效能的设计提供了理论指导.     

求解Cahn-Hilliard方程非线性项的两种数值格式对比

基于快速显式算子分裂方法,将Cahn-Hilliard方程与分子束外延(MBE)方程分裂为非线性与线性两个部分.对非线性部分,采用中心差分与半离散有限差分两种格式进行数值计算;线性部分通过拟谱方法进行精确求解.在两种格式下,通过对数值解的全局L~∞误差估计,比较分析了两种格式的数值解差异以及运行效率.对于Cahn-Hilliard方程与MBE方程,两种格式的数值解一致;对Cahn-Hilliard方程的数值求解,中心差分格式的效率是半离散有限差分格式的3到6倍;在MBE方程的数值求解中,半离散有限差分格式的效率是中心差分格式的2倍.     

基于MATLAB的静态场边值问题有限差分法的研究

有限差分法是求解静态场边值问题的一个非常有效的数值解法,它是将求解区域划分为有限个网格点,用一组差分方程代替原来一组微分方程.该方法求得的是近似解而不是精确解.求解区域内网格划分大小关系着计算的精确度,网格尺寸划分越小,计算精确度越高;反之,精确度越低.本文运用MATLAB语言使得有限差分法求解区域内电势分布的解法变得简单、易行,摆脱了传统方法使用C语言较复杂的缺陷.通过仿真验证了算法和程序的有效性.     

多相图像分割的Split-Bregman方法及对偶方法

变分水平集方法为多相图像分割提供了统一框架,但其能量泛函的局部极值问题和较低的计算效率制约着该类方法的应用,文中针对此问题提出一种改进模型和方法.首先将两相图像分割的全局凸优化模型推广到多相图像分割,建立了多相图像分割的交替凸优化变分模型,以改善传统模型的局部极值问题;然后提出了相应的快速Split-Bregman方法和对偶方法来提高计算效率,其中Split-Bregman方法通过引入辅助变量将凸松弛后的变分问题转化为简单的Poisson方程和精确的软阈值公式,对偶方法则通过引入对偶变量将该问题转化为对偶变量的半隐式迭代计算和主变量的精确计算公式.文中的改进模型适用于任意多相图像分割,且对二维和三维图像分割具有相同形式,可用于三维图像的多对象自动形状恢复.最后通过多个数值算例验证了文中方法的计算效率优于传统的方法.     

MATLAB 和VC ++联合编程的COM 研究

VC+ +在实现矩阵运算、数值分析、工程计算等方面比较复杂,应用VC+ + 与MATLAB 混合编程方法可以充分发挥VC+ + 和MATLAB 各自优势,提高仿真和开发效率。着重介绍了利用组件对象模型(COM) 技术的VC+ + 与MATLAB 的联合编程方法,阐述了该方法实现过程,并通过两个具体应用实例加以验证。实验仿真结果表明,采用联合编程的COM 技术能快速直观地得到满意结果,对求解矩阵运算、数值分析、工程计算等问题是行之有效的。     

一种高效的快速近似控制向量参数化方法

控制向量参数化(Control vector parameterization, CVP) 方法是目前求解流程工业中最优操作问题的主流数值方法,然而,该方法的主要缺点之一是 计算效率较低,这是因为在求解生成的非线性规划(Nonlinear programming, NLP) 问题时,需要随着控制参数的调整,反复不断地求解相关的微分方程组,这也是CVP 方法中最耗时的部分.为了提高CVP 方法的计算效率,本文提出一种新颖的快速近似方法,能够有效减少微分方程组、函数值以及 梯度的计算量.最后,两个经典的最优控制问题上的测试结果及与国外成熟的最优控制 软件的比较研究表明:本文提出的快速近似CVP 方法在精度和效率上兼有良好的表现.     

基于Potts模型的隐式曲面上的图像分割方法

针对隐式曲面上多相图像分割的问题,基于曲面的隐式表达、隐式曲面上的内蕴梯度等概念,将用于平面图像分割的Potts模型推广.首先对于隐式封闭曲面和隐式开放曲面,分别给出Potts模型的推广形式.然后对于传统梯度降方法计算效率低的问题,为曲面上的Potts模型设计了Split Bregman算法和对偶方法,并在对偶方法的基础上提出了一种改进的快速算法.多个数值实验结果表明,所提出的曲面上的Potts模型能有效地分割闭/开曲面上的分段常值图像,并且新的改进对偶方法在计算效率方面优于其他两种方法.     

改进CV模型图像分割的Split-Bregman方法

水平集方法中的Chan-Vese模型（简称CV模型）对灰度不均匀及边界对比度低的图像的分割效果不够精确,计算效率也不是很高。针对灰度不均匀引入偏差场来修正CV模型中的区域平均灰度并引入核函数来加权能量泛函。针对计算效率低下的问题,在上述基础上得出其全局凸分割模型（Global Convex Segmentation,GCS）,用Split-Bregman迭代求解该模型。实验结果表明：改进后的模型提高了分割精确度和计算效率。     

Extension of CE/SE method to 2D viscous flows

The space–time conservation element–solution element (CE/SE) method is extended to two-dimensional viscous flow problems. The formulation is presented and discussed. The extended CE/SE method is applied to several 2D viscous flow problems, such as boundary layer flow, entrance of channel flow, backward facing step flow and cavity flow. The numerical results and their comparison with analytical result and experimental data are presented. The capability of this method for predicting viscous flow feature and heat transfer is demonstrated. Also the capability of the method to solve both high-speed flows and low-Mach number flows is demonstrated.     

On numerical stabilization in the solution of Saint-Venant equations using the finite element method

Solving the Saint-Venant equations by using numerical schemes like finite difference and finite element methods leads to some unwanted oscillations in the water surface elevation. The reason for these oscillations lies in the method used for the approximation of the nonlinear terms. One of the ways of smoothing these oscillations is by adding artificial viscosity into the scheme. In this paper, by using a suitable discretization, we first solve the one-dimensional Saint-Venant equations by a finite element method and eliminate the unwanted oscillations without using an artificial viscosity. Second, our main discussion is concentrated on numerical stabilization of the solution in detail. In fact, we first convert the systems resulting from the discretization to systems relating to just water surface elevation. Then, by using M-matrix properties, the stability of the solution is shown. Finally, two numerical examples of critical and subcritical flows are given to support our results.     

求解应力强度因子的样条虚边界元交替法

为求解平面裂纹问题的应力强度因子,提出基于Muskhelishvili基本解和样条虚边界元法的样条虚边界元交替法.该方法将平面内带裂纹有限域问题分解成带裂纹无限域问题与不带裂纹有限域问题的叠加.带裂纹无限域问题利用Muskhelishvili基本解法直接得出,不带裂纹有限域问题采用样条虚边界元法求解.利用该方法对复合型中心裂纹方板和I型偏心裂纹矩形板进行分析.数值结果表明该方法精度高且适用性强.     

An improved CE/SE scheme for numerical simulation of gaseous and two-phase detonations

A new structure of solution elements and conservation elements based on rectangular mesh was proposed and an improved space-time conservation element and solution element (CE/SE) scheme with second-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas-droplet) detonation. Shock reflections were simulated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas-droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C-J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular patterns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.     

Mixed finite element method for analysis of viscoelastic fluid flow

In the present paper, numerical analysis of incompressible viscoelastic fluid flow is discussed using mixed finite element Galerkin method. Because Maxwellian viscoelasticity is assumed as the constitutive equation, stress components could not be eliminated from the governing equation system. Because of this, mixed finite element method is utilized to discretize the basic equations. For the solution procedures to solve discretized equation system, Newton-Raphson method for steady flow and perturbation method for unsteady flow is employed. As the numerical examples, comparison was made on the finite element computational results between by direct method and by mixed method. Effects of the viscoelasticity is analyzed for the flows at Reynold's numbers 30, 50 and 70.     

Numerical solutions of the one-phase classical Stefan problem using an enthalpy green element formulation

The enthalpy method is exploited in tackling a heat transfer problem involving a change of state. The resulting governing equation is then solved with a hybrid finite element - boundary element technique known as the Green element method (GEM). Two methods of approximation are employed to handle the time derivative contained in the discrete element equation. The first involves a finite difference method, while the second utilizes a Galerkin finite element approach. The performance of both methods are assessed with a known closed form solution. The finite element based time discretization, despite its greater challenge, yields less reliable numerical results. In addition a numerical stability test of both methods based on a Fourier series analysis explain the dispersive characters of both techniques, and confirms that replication of correct results is largely attributed to their ability to handle the harmonics of small wavelengths which are usually dominant in the vicinity of a front.     

Finite element procedures for nonlinear structures in moving coordinates. Part 1: Infinite bar under moving axial loads

This paper deals with analyzing nonlinear structures under high-speed moving loads by use of the finite element method. The stationary response of an infinite bar posed on a Winkler foundation under constant moving loads is investigated. Instead of the transient analysis, the stationary solution of this problem is obtained by solving a static system in a reference frame which moves with the load for reducing the computation cost. To overcome the difficulty due to numerical instabilities when considering very fast loads (supersonic loads), a new procedure to govern the finite element formulation in moving coordinates is proposed. Comparing numerical solutions with analytical ones shows that the proposed method is valid for all values of load speed. Last, an example of nonlinear elastic foundation is considered to outline the nonlinear effects.     

Green element computation of the Sturm-Liouville equations

A mathematical derivation of a new numerical procedure called the Green element method (GEM) is presented and applied to the solution of Sturm-Liouville problems. The GEM is a numerical technique which expands the scope of application of the boundary element method (BEM) by implementing the singular boundary integral theory in an element-by-element fashion; and like the finite element method (FEM) gives rise to a banded coefficient matrix which is easy to handle numerically. For this application, the location of both the field and the source nodes within the same element makes it possible for integrations to be carried out accurately, thereby enhancing the accuracy of discrete equations. The method is therefore easy to apply and, because of its domain based implementation, it maintains the flexibility of the FEM. We apply the GEM to the solution of boundary value differential equations which represent the form of Sturm-Liouville problems, and its capability is demonstrated by comparing the results with those of the finite element methods available in the literature. Satisfactory results and a second-order accuracy were found to be exhibited.     

A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty

Real life convection-diffusion problems are characterized by their inherent or externally induced uncertainties in the design parameters. This paper presents a spectral stochastic finite element semi-Lagrangian method for numerical solution of convection-diffusion equations with uncertainty. Using the spectral decomposition, the stochastic variational problem is reformulated to a set of deterministic variational problems to be solved for each Wiener polynomial chaos. To obtain the chaos coefficients in the corresponding deterministic convection-diffusion equations, we implement a semi-Lagrangian method in the finite element framework. Once this representation is computed, statistics of the numerical solution can be easily evaluated. These numerical techniques associate the geometrical flexibility of the finite element method with the ability offered by the semi-Lagrangian method to solve convection-dominated problems using time steps larger than its Eulerian counterpart. Numerical results are shown for a convection-diffusion problem driven with stochastic velocity and for an incompressible viscous flow problem with a random force. In both examples, the proposed method demonstrates its ability to better maintain the shape of the solution in the presence of uncertainties and steep gradients.