三维非牛顿熔体前沿界面的Level Set/Ghost/SIMPLEC模拟

建立了三维粘性不可压非牛顿流体流动的控制方程,采用Level Set/Ghost/SIMPLEC方法模拟了注塑成型充模阶段的三维流动过程;追踪到了不同时刻的熔体前沿界面,预测并分析了流动过程中不同时刻的压力、速度等重要的流动特征参数,并与牛顿流体相应的流动特征参数做了对比.研究结果表明:Lovol Set/Ghost/SIMPLEC方法可以准确追踪非牛顿熔体前沿界面:幂律熔体在流动过程中的压差明显大于牛顿熔体的压差,沿横截面的速度分布也有明显的差别.     

用Level Set方法追踪运动界面

首先介绍了近年来发展起来的界面追踪技术Level Set方法,然后采用五阶WENO格式和积分平均型TVD格式计算Level Set方程,用修正的Godunov方法求解重新初始化的Level Set方程,数值求解了同心圆在常数流场,圆和矩形界面在剪切流场,缺口圆在旋转流场中的界面变形和还原效果,比较了时间导数离散精度和Level Set函数有无重新初始化对界面追踪效果的影响．最后,通过和其它界面处理方法的比较可以看出,Level Set方法不仅能够比较准确地追踪运动界面,而且无须进行复杂繁琐的界面重构技术,容易编程,具有较大的通用性．     

基于四阶半离散中心迎风格式的虚拟流方法的应用

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,因此再将新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。     

Level Set方法和多介质可压缩流

多介质可压缩流问题计算的关键是如何精确的捕获不同时刻物质界面的位置,从而将多介质问题分解成多个单介质问题去处理.Level Set方法的优点是不用显示的追踪物质界面,而用距离函数就能精确定位界面.同时,用Level Set方法追踪界面运动易于处理界面拓扑结构的变化、易于处理大变形问题.本文成功地将Level Set方法应用在二维多介质可压缩流计算.     

求解无粘可压Euler方程组的虚拟流方法

首先将三阶Godunov型半离散中心迎风格式推广到四阶,之后再将该新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法结合起来,成功地处理了非反应激波问题和多介质流中的爆轰间断问题。由于Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,故而本文的方法可以很自然地推广到多维情况。     

基于Level Set的多维双曲守恒律标量方程的激波追踪方法

结合四阶CWENO(Cemral Weighted Essentially Non-Oscillatory)格式、四阶NCE(Natural Continuous Extensions)Runge-Kutta法和Level Set方法，很好地处理了一维双曲守恒律标量方程的激波追踪问题。针对二维双曲守恒律标量方程，成功地用五阶WENO格式、非TVD格式的四阶Runge-Kutta方法和Level Set方法进行激波追踪。将所得的数值解与标准的高阶激波捕捉方法所得的数值解进行比较，说明基于Level Set的激波追踪方法的有效性与逐点收敛性。     

带有障碍物溃坝流动问题的有限元数值模拟研究

针对下游带有障碍物的溃坝流动问题,本文基于两相流动模型,在有限元算法框架下对其进行数值模拟研究。依据水平集(Level Set)方法追踪运动界面,并引入了一个简单的修正技术,保证较好的质量守恒性。为了精确表示运动界面,采用稳定和有效的间断有限元方法求解双曲型Level Set及其重新初始化方程。对于两相统一Navier-Stokes方程,首先利用分裂格式对其解耦,然后通过SUPG (Streamline Upwind Petrov Galerkin)方法进行数值求解。模拟研究了下游带有障碍物的牛顿流体溃坝流动问题,得到的数值结果与文献已有模拟结果及实验结果均吻合较好。此外,还考虑了幂律型非牛顿流体,并分析了不同特性非牛顿流体对于溃坝流动过程和界面形态等的影响。     

钝感炸药爆轰波传播和驱动的数值模拟研究

为实现对非理想爆轰波传播和爆轰驱动问题的精确计算,研究了与贴体坐标下Level Set方法相结合的爆轰冲击波动力学(DSD)计算方法;根据Hamilton-Jacobi方程的Godunov差分格式,提出了非正交的贴体坐标系中Level Set函数方程的差分格式及其相应的数值方法;并将该DSD方法与二维流体动力学程序TD...     

气液两相流动与固壁相互作用耦合求解的研究

气液两相流动与固壁相互作用的研究是液滴撞击壁面运动研究的重要基础.以结合了VOF和Level Set两种方法优点的用于气液相界面追踪的复合Level Set-VOF方法和利用唯象分析方法建立的能够反映接触角滞后性及壁面性质对润湿过程影响的壁面润湿模型为基础,提出了气液两相流动与固壁相互作用耦合求解流程,给出了气液两相流动与固壁相互作用耦合求解过程中接触线速度的计算方法及边界条件的确定方法.通过与已有实验结果的对比,对提出的气液两相流动与固壁相互作用耦合求解方法的有效性进行了验证.     

Level Set方法在地面效应数值模拟中的应用

利用Level Set方法隐式捕捉界面并能处理复杂的物质界面及其拓扑结构变化（如合并、交叉、破碎等）情况的优势,基于可压缩N-S方程的预处理技术,采用基于界面两侧介质黎曼关系的修正虚拟流体方法对介质边界进行处理;将只能应用于可压缩流动界面模拟的修正虚拟流体方法推广应用于不可压缩流动问题的模拟,数值模拟了气-水运动界面与近水面飞行器的相互影响规律。通过与将水面视为对称面的简化模型对比发现：利用自由运动界面模型计算的NACA6409翼型升力较小,能更准确地反映飞行器流场对水面形状的影响,其结果更为符合实际;文中还对比了翼型距水面不同高度时的结果,得到了翼型受水面影响的强弱与翼型距水面的高度成反比的结论。     

基于黏弹性的微注射成型流动模拟

应用有限元方法研究了微注射成型中瞬态、可压缩、非牛顿熔体流动的黏弹性对流动前沿及流动平衡的影响。基于Phan-Thien-Tanner模型建立了熔体流动的本构方程,利用Hele-Shaw假设和简化建立了瞬态、可压缩、非牛顿熔体流动的连续性方程、动量方程、能量方程;为了有效地描述微注射成型的尺寸效应,采用了边界滑移和表面张力边界条件。通过分部积分和待定系数法导出了带有边界信息的变分方程和求解应力分量的半解析公式,构造了有限元离散求解及超松驰迭代算法。模拟结果表明:熔体的黏弹性对浇口附近的压力和后续的熔体流动前沿有重要影响;与黏性模型相比,黏弹性模型可以控制模拟压力的快速增长,减少不同型腔之间的充填差异,与短射实验结果也更吻合。     

引入工艺因素的汽车车身部件碰撞仿真分析

采用自主开发的高效快速的逆成形有限元分析方法和网格映射技术,并与碰撞仿真技术相结合,提出了引入工艺因素、又保证设计周期、提高碰撞仿真精度的汽车车身及部件“精细”仿真分析方法.以某轿车中的主要碰撞承载和吸能部件左前纵梁为例,采用一步逆算有限元法和LS-DYNA软件对其进行基于引入工艺因素的碰撞仿真分析.结果表明:为了提高碰撞分析的精度,在汽车车身碰撞仿真中需要采用考虑冲压成形效应的碰撞分析方法,其中影响程度最大的因素是等效塑性应变.     

Outward spherical solidification of a superheated melt with time dependent boundary flux

Short-time analytical solutions of solid and liquid temperatures and freezing front have been obtained for the outward radially symmetric spherical solidification of a superheated melt. Although results are presented here only for time dependent boundary flux, the method of solution can be used for other kinds of boundary conditions also. Later, the analytical solution has been compared with the numerical solution obtained with the help of a finite difference numerical scheme in which the grid points change with the freezing front position. An efficient method of execution of the numerical scheme has been discussed in details. Graphs have been drawn for the total solidification times and temperature distributions in the solid.     

气体辅助注射成型过程动力学分析

基于气体穿透机理和Hele-Shaw流动模型,对管状模腔中气体冲破熔体前沿形成中空制品气辅成型过程进行了研究,推导出反映充模流动压力梯度比、非牛顿幂率指数等影响因素与计算表层熔体厚度比之间关系的数学公式,建立了熔体前沿和气体前沿速度与位移演化关系的数学模型,分别得出了牛顿流体和非牛顿流体选取不同影响参数时熔体前沿和气体前沿速度、位移的演化曲线.模拟结果表明,所建数学模型能较好的反映熔体前沿和气体前沿速度、位移演化关系.在气体冲破熔体前沿以前,气体接近匀加速运动,前沿位移梯度逐渐增加;熔体前沿的速度几乎保持不变,位移随时间接近线性增长.当气体冲破熔体前沿时,熔体和气体前沿的速度和位移均急速上升.     

成型充填过程的ALE有限元模拟

在ALE框架中提出了一个用于成型充填过程有限元数值模拟的模型。应用ALE参考构形及ALE参考粒子速度描写充填过程中的熔体质量运动。摒弃了Hele-Shaw近似假定,因而所提出的模型能用于非薄壁型腔中高分子材料充填过程的数值模拟。应用基于时域分步算法的Taylor-Galerkin方法,对控制成型充填过程的守恒方程建立了弱形式。对移动自由面附近的充填材料区构造了网格生成算法与网格重划分方案。给出了在几种不同形状的典型腔体中充填过程的数值模拟结果,表明了所提出的ALE有限元模型模拟充填过程的有效性。     

Opening of a system of cracks—on the mechanism of the cyclic lateral eruption of the St. Helens volcano in 1980

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.     

High‐order upwind compact scheme and simulation of turbulent premixed V‐flame

A high‐order accurate upwind compact difference scheme with an optimal control coefficient is developed to track the flame front of a premixed V‐flame. In multi‐dimensional problems, dispersion effect appears in the form of anisotropy. By means of Fourier analysis of the operators, anisotropic effects of the upwind compact difference schemes are analysed. Based on a level set algorithm with the effect of exothermicity and baroclinicity, the flame front is tracked. The high‐order accurate upwind compact scheme is employed to approximate the level set equation. In order to suppress numerical oscillations, the group velocity control technique is used and the upwind compact difference scheme is combined with the random vortex method to simulate the turbulent premixed V‐flame. Distributions of velocities and flame brush thickness are obtained by this technique and found to be comparable with experimental measurement. Copyright © 2005 John Wiley & Sons, Ltd.     

Fhree-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD

Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.     

Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD

Based on the successive iteration in the Taylor series expansion method,a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper.Numerical characteristics of the scheme are studied by the Fourier analysis. Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node,the proposed scheme is explicit and can achieve arbitrary order of accuracy in space.Application examples for the convection- diffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given.It is found that the proposed compact scheme is not only simple to implement and economical to use,but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.     

两相介质中火焰诱导激波现象的研究

基于双流体模型，采用跟踪法处理火焰内边界，ＴＶＤ格式计算气相激波，ＭａｃＣｏ－ｍａｃｋ格式计算颗粒相流场，对两相可燃介质中火焰诱导激波现象进行了理论分析与实验模拟，研究了颗粒相参数对火焰诱导激波现象的影响。