基于八叉树自适应网格技术的Level Set运动界面追踪方法

Level Set方法因能有效地处理界面处复杂的拓扑结构变化以及大变形问题,广泛应用于界面追踪领域。在Level Set方法追踪运动界面时引入八叉树网格技术,通过八叉树网格的细化和粗化技术减少计算网格数量和计算内存并提高计算效率和计算精度。因为八叉树网格为非均匀网格,其相邻网格的层数值可能不相同,所以不能直接采用WENO格式离散Level Set函数得到网格处的函数值,进而提出八叉树网格离散模型解决这一问题,并提出基于八叉树网格距离场重新初始化方法减少Level Set方法的质量损失,最后将基于八叉树网格技术的Level Set方法应用于两个给定速度场的运动界面模拟算例以及基准件方腔的铸造充型过程的模拟。模拟结果表明该方法可以提高界面的精度,同时改善质量守恒性。     

基于四叉树直角坐标网格的运动界面追踪方法

运动界面的追踪是两相流模拟中需要解决的主要问题之一。基于四叉树直角坐标网格实现了Level set界面追踪方法和网格的局部自适应控制。通过模拟3个给定速度场(平移流场、旋转流场、剪切流场)的运动界面追踪问题,证明了自适应四叉树直角坐标网格与Level set方法结合的优势。     

基于四叉树直角坐标网格的运动界面追踪方法

运动界面的追踪是两相流模拟中需要解决的主要问题之一。基于四叉树直角坐标网格实现了Level set界面追踪方法和网格的局部自适应控制。通过模拟3个给定速度场（平移流场、旋转流场、剪切流场）的运动界面追踪问题,证明了自适应四叉树直角坐标网格与Level set方法结合的优势。     

三维熔体前沿界面的Level Set追踪

给出三维Level Set方程,采用五阶加权本质无振荡格式进行空间离散,通过算例验证了该算法的正确性及追踪三维运动界面的准确性。进而将Level Set算法和同位网格有限体积法进行耦合,模拟了注塑成型充填阶段的三维流动过程,准确追踪到了不同时刻熔体前沿界面,预测并分析了流动过程中不同时刻的压力、速度等重要流动特征。数值结果表明,该方法可追踪三维熔体前沿界面,预测充填过程中的重要流动特征。     

Pseudo-Anosov映射作用下拓扑混沌数值模拟

对方腔内3个方形搅拌轴两两交替运动引发的Stokes流动的混合问题进行了数值模拟研究。提出了两种搅拌轴方形运动路径来引发相空间内Pseudo-Anosov（pA）映射。采用有限体积方法求解速度场,搅拌轴的周期性速度边界借助叠加网格技术来实现。流动区域采用交错网格划分,控制方程组采用具有二阶精度的中心差分格式离散。粒子运动前锋追踪计算采用具有四阶精度的Runge-Kutta方法实现。得到了Poincaré截面,表明pA起作用的空间尺度几乎覆盖整个方腔,只有4个角区域除外。计算了不同初始位置的示踪剂演化图像来表征混合过程。示踪剂增长将经历指数增长,其增长指数大于pA映射矩阵的预测值,这是由于搅拌轴形状、运动路径等流场细节导致的示踪剂界面局部二次折叠拉伸造成的。     

复杂两相流中界面追踪方法——VOSET的性能分析

界面追踪方法-VOSET(coupled Volume-of-Fluid and Level Set method)结合了VOF和Level Set两种方法的优点,克服了这两种方法的缺点.VOSET方法采用VOF方法捕捉两相间的界面,保持了两相间的质量守恒,克服了Level Set方法质量不守恒的缺点;利用几何计算方法...     

气辅注射成型运动界面的Level Set方法数值模拟

给出气液两相流数学模型,选取Cross-WLF模型作为熔体的黏度模型,采用Level Set/SIMPLEC方法模拟了气体辅助注射成型中气体穿透过程,追踪到了不同时刻的运动界面(气熔界面和熔体前沿界面),描述了运动过程中不同时刻速度和温度等重要物理量的分布情况,分析了熔体温度、气体延迟时间和注射压力对气体穿透时间和穿透长度的影响。数值结果表明,Level Set/SIMPLEC方法可以准确追踪气体穿透过程中的两个运动界面;熔体温度、延迟时间和气体注射压力对气体穿透长度有显著影响。     

熔体充模过程动态模拟及流场分析

将Level Set／Ghost方法应用于聚合物成型研究，实现了非等温情况下注射成型聚合物熔体充模阶段的动态模拟；得到了正确的流线分布和不同时刻的温度、压力等值线分布。对Level Set／Ghost方程的求解，空间方向采用高分辨率、稳定且无振荡的5WENO（the fifth—order weighted essentially non—oscillatory）格式进行离散，时间方向采用稳定的TVD-RK（total variation diminishing Runge Kutta）方法进行离散。物理量控制方程采用一般的有限差分格式进行数值求解。结果表明，Level Set／Ghost方法可以准确追踪非等温聚合物熔体前沿界面的位置，并能精确描述前沿界面的形状，同时可以实现动态流场物理量的准确模拟。     

基于Fluent的三维注塑充填界面追踪方法研究

充填阶段是注塑成型中最复杂也是最重要的阶段。考虑到Moldflow软件在注塑成型模拟中的局限性,越来越多的学者使用Fluent等通用计算流体动力学(CFD)软件进行注塑成型模拟。然而,大多数基于通用CFD软件的注塑充填模拟中都忽略了气体相。基于Fluent软件实现了三维注塑充填模拟,并将没有考虑空气相,以及考虑空气相时使用两种不同界面追踪方法的模拟结果分别与Moldflow进行了对比。结果表明,在基于Fluent的注塑充填模拟中应该考虑空气,且使用流体体积函数(VOF)和水平集(Level Set)的耦合方法 (CLSVOF)比单纯的VOF方法界面追踪效果更好。     

短纤维增强熔体三维充模模拟及制品性能预测

基于气-液-固三相模型,给出了适用于三维流场的纤维质心虚拟速度、纤维平动与取向、动量交换源项的求解公式,建立了描述短纤维增强聚合物熔体充模过程的三维模型。采用同位网格有限体积法和Level Set界面追踪技术,实现了充模过程的三维动态模拟。并且,根据模拟计算出的平均取向角,提出了三维取向短纤维增强复合材料力学性能参数计算的一种简化模型。数值结果表明:三维模拟技术可有效反映注塑成型充模的流动过程和喷泉效应;纤维取向分析可量化显示纤维在型腔中的表层-芯层结构取向;弹性模量计算结果与实验结果吻合较好。     

Moving mesh generation for tracking a shock or steep moving front

For tracking a shock or steep moving front in the numerical solution of Partial Differential Algebraic Equations (PDAEs), an accurate spatial discretization method, Weighted Essentially Non-Oscillatory (WENO) scheme, is combined with moving grid techniques so that spacing of moving meshes is smoothed locally and globally. Several monitor functions, as metric criteria of node concentration, are examined. While the fixed grid method (uniform grid size) needs many mesh points to obtain enough solution accuracy, the moving grid method (non-uniform grid size) enhances accuracy even at small mesh numbers but it may be prohibitive owing to the addition of complex and non-linear mesh equations into physical PDAEs. The combination of the WENO scheme (based on an adaptive stencil idea) with the moving grid techniques improves stability and accuracy in the numerical solution over the commonly used moving grid method of central discretization. To locate adequate grid position in the moving mesh method, suitable monitor function according to problems must be selected.     

固体溶质溶解过程自然对流非稳态数值模拟

利用多物理场耦合分析软件Comsol Multiphysic 3.5及其动网格技术,结合传质学相关理论对固体溶质溶解过程进行了直接数值模拟.考虑了溶解过程中液相部分的自然对流,溶解引起的其表面形态的变化由溶解质量与相界面处的浓度梯度的关系建立的方程描述.研究结果表明:文中方法可以很好地捕捉由于溶解引起的界面运动和变形的...     

A fast and accurate numerical method for solving simulated moving bed (SMB) chromatographic separation problems

Solving simulated moving bed (SMB) chromatography models requires fast and accurate numerical techniques, since their system size computed is large due to multi-columns and multi-components, in addition the axial solution profiles contain steep moving fronts.The space-time conservation element/solution element (CE/SE) method addressed in this study enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level) on staggered space-time grids. Thus, accurate and computationally efficient numerical solutions are obtained. Stable solutions are guaranteed if the Courant-Friedrichs-Lewy (CFL) condition is satisfied. The boundary condition and recycle flow treatments are much simpler than for the time integrator in the framework of the method of lines. Applying the CE/SE method for SMB chromatographic problems, non-dissipative and accurate solutions are obtained and fast calculation is achieved in this study.The effects of two-computational parameters (CFL number and mesh stepsize) on the numerical solution are examined, illustrating two SMB processes whose Peclet and Stanton numbers are different. It is shown that the CFL number affects little the numerical solution under the relatively high Peclet number and low Stanton number but a small mesh stepsize is required to enhance accuracy. As the Peclet number decreases and the Stanton number increases, a lower CFL number is preferable and larger mesh stepsize is permitted. In the case study of the SMB adsorption problems, a large CFL number and sufficient number of mesh points (or small mesh stepsize) are desirable to reduce the calculation time and increase accuracy.     

On a pure finite-element-based methodology for resin transfer molds filling simulations

A physically accurate and computationally effective pure finite-element-based methodology for Resin Transfer Molding (RTM) process simulations is presented. The formulations are developed starting with the time-dependent mass conservation equation for the resin flow. Darcy's flow approximations are invoked for the velocity field, thereby forming a transient governing equation involving the pressure field and the resin saturation fill factor which tracks the location of the resin front surface. Finite element approximations are then introduced for both the fill factor and the pressure field, and the resulting transient discrete equations are solved in an iterative manner for both the pressures and the fill factors for tracking the progression of the resin front in an Eulerian mold cavity. The formulation involves only a pure finite-element Eulerian mesh discretization of the mold cavity and does not require specification of control volume regions and has no time increment restrictions that exist as in the traditional explicit finite-element-control volume based formulations. The present formulations accurately account for and capture the physical transient nature of the mold-filling process while maintaining improved numerical and computational attributes. Mold-filling simulations involving various geometrically complex mold configurations are presented, demonstrating the applicability of the developments for practical manufacturing process simulations.