Euler-Lagrange耦合计算的GEL方法

研究了一种Euler-Lagrange耦合数值方法ghost-fluid Euler-Lagrange(GEL)方法,编写了GEL二维计算程序。其中Euler流场计算采用以SCB格式编制的二阶计算程序,Lagrange域计算采用DEFEL二维动力有限元程序。通过一维黎曼问题的计算结果与高精度PPM方法进行的比较,以及二维移动边界cylinder lift-off problem的计算结果与文献的对比,验证了GEL方法和本文程序的正确性。     

GEL方法在一维双界面问题中的应用

用ghost-fluid Euler-Lagrange(GEL)耦合数值方法,对二维GEL计算程序(其中Euler流场计算采用以SCB格式编制的二阶计算程序,Lagrange域计算采用DEFEL二维动力有限元程序)进行扩展,将程序应用于多界面问题.算例为空气和水的一维双界面黎曼问题,获得了密度、速度和压力结果,并通过i...     

平面二次包络弧面蜗杆传动有限元分析

本文首先应用弹性接触有限元混合法,通过大量上机计算,求解了平面二次包络弧面蜗杆传动的齿间载荷分配,提出了一种把这类关于齿间载荷分配的三维弹性接触问题简化为二维问题的方法,修改编写了二维等参元弹性接触有限元混合法等四个计算程序。 同时本文还求解了受载情况最恶劣的轮齿的位移场和应力场。对计算结果进行了分析讨论。     

平面二次包络弧面蜗杆传动有限元分析

本文首先应用弹性接触有限元混合法,通过大量上机计算,求解了平面二次包络弧面蜗杆传动的齿间载荷分配,提出了一种把这类关于齿间载荷分配的三维弹性接触问题简化为二维问题的方法,修改编写了二维等参元弹性接触有限元混合法等四个计算程序。 同时本文还求解了受载情况最恶劣的轮齿的位移场和应力场。对计算结果进行了分析讨论。     

软岩三维非线性统一弹粘塑性本构模型有限元分析

在作者已建立的软岩三维非线性统一弹粘塑性软化本构模型基础上,讨论了软岩三维非线性统一弹粘塑性本构模型有限元分析过程,即推导了软岩三维非线性统一弹粘塑性屈服面(破坏面)的流动矢量表达式,便于编程与通用的有限元程序接口,进行二次开发;利用张量求导的原则,导出了流动矢量对应力求导公式中关键矩阵的具体表达式,并结合平面应力、平面应变和轴对称问题的特点进行了简化,得出了适合于分析二维问题的关键矩阵的表达式;采用流动矢量奇异性的统一处理方法,有效地处理了各种角点奇异性问题;最后给出了有限元分析的流程图,便于编制有限元程序.     

杆杆型冲击拉伸试验装置的二维轴对称弹塑性有限元分析

对带有哑铃状圆柱形试件的杆杆型冲击拉伸试验装置,建立了含有多个物理和几何间断面的二维轴对称弹塑性有限元模型,采用动态增量非线性有限元程序ＡＤＩ－ＮＡ,进行了数值模拟模拟分析,揭示了应力波在试验系统中的传播规律,在弹性框架内初步论证了杆杆型冲击拉伸试验装置测试原理的有效性。     

二维流体力学有限差分和有限元程序的耦合计算

根据压力和法向速度连续准则,将Euler方法为基础的MFPPM（Piecewise-Parabolic Method）程序和Lagrange方法为基础的DEFEL（2-D Finite ElementsCode,二维流体弹塑性动力有限元）程序进行耦合,发展了基于levelset的GEL（Ghost—fluid Euler-Lagrange）方法。该方法在处理大变形流场与小变形结构以及复杂流动与多物体相互作用等问题具有优越性。通过二维算例的计算结果与文献比较,检验了GEL方法和耦合程序的正确性,并对水下爆炸形成的流场对多物体作用过程进行了数值模拟。     

基于能量等效原理的应变局部化分析:Ⅱ.有限元解法

以非局部塑性理论为基础,应用状态空间理论,通过局部和非局部两个状态空间的塑性能量耗散率等效原理,提出了一种求解应变局部化问题的新方法,以得到与网格无关的数值解.针对二维问题的屈服函数和流动法则导出了求解非局部内变量的一般方程,并提出了在有限元环境中求解应变局部化问题的应力更新算法.为了验证所提出的方法,对1个一维拉杆和3个二维平面应变加载试件进行了有限元分析.数值结果表明,塑性应变的分布和载荷-位移曲线都随着网格的变小而稳定地收敛,应变局部化区域的尺寸只与材料内尺度有关,而对有限元网格的大小不敏感.对于一维问题,当有限元网格尺寸减小时,数值解收敛于解析解.对于二维剪切带局部化问题,数值解随着网格尺寸的减小而稳定地向唯一解收敛.当网格尺寸减小时,剪切带的宽度和方向基本上没有变化.而且得到的塑性应变分布和网格变形是平滑的.这说明,所提方法可以克服经典连续介质力学模型导致的网格相关性问题,从而获得具有物理意义的客观解.此模型只需要单元之间的位移插值函数具有C~0连续性,因而容易在现有的有限元程序中实现而无需对程序作大的修改.     

液体三维晃动特征问题的有限元数值计算方法

本文采用有限元方法数值求解任意刚性容器内液体三维晃动的固有频率和模态。通过建立液体晃动特征问题的泛函极值原理，编制了四面体等参单元有限元程序，计算了平放圆柱腔内三维液体晃动的特征频率，并将矩形容器、球腔、带“十”字隔板球形容器内的液体三维晃动计算结果与解析解、实验结果和二维有限元数值解进行了比较，程序的正确性得到了验证。     

有限元离散模型中的出平面波动

采用分离变量技术,将二维出平面(Anti-Plane)波动问题的有限元运动方程化为两个联立的一维方程,获得了这一离散模型中波动的解析解,由此对有限元离散模型中出平面波动问题进行了深入的研究。分析了出平面弹性波的频散、截止频率、寄生振荡和有限元离散化引起的波传播的附加的各向异性性质等,同时讨论了时域离散化对出平面波动规律的影响。     

Two‐dimensional non‐Newtonian injection molding with a new control volume FEM/volume of fluid method

A new method based on volume of fluid for interface tracking in the simulation of injection molding is presented. The proposed method is comprised of two main stages: accumulation and distribution of the volume fraction. In the first stage the equation for the volume fraction with a noninterfacial flux condition is solved. In the second stage the accumulated volume of fluid that arises as a consequence of the application of the first one is dispersed. This procedure guarantees that the fluid fills the available space without dispersion of the interface. The mathematical model is based on two‐phase transport equations that are numerically integrated through the control volume finite element method. The numerical results for the interface position are successfully verified with analytical results and numerical data available in the literature for one‐dimensional and two‐dimensional domains. The transient position of the advance fronts showed an effective and consistent simulation of an injection molding process. The nondispersive volume of fluid method here proposed is implemented for the simulation of nonisothermal injection molding in two‐dimensional cavities. The obtained results are represented as transient interface positions, isotherms and pressure distributions during the injection molding of low density polyethylene. Copyright © 2012 John Wiley & Sons, Ltd.     

Front‐tracking by the level‐set and the volume penalization methods in a two‐phase microfluidic network

Two‐phase immiscible fluids in a two‐dimensional micro‐channels network are considered. The incompressible Stokes equations are used to describe the Newtonian fluid flow, while the Oldroyd‐B rheological model is used to capture the viscoelastic behavior. In order to perform numerical simulations in a complex geometry like a micro‐channels network, the volume penalization method is implemented. To follow the interface between the two fluids, the level‐set method is used, and the dynamics of the contact line is modeled by Cox law. Numerical results show the ability of the method to simulate two‐phase flows and to follow properly the contact line between the two immiscible fluids. Finally, simulations with realistic parameters are performed to show the difference when a Newtonian fluid is pushed by a viscoelastic fluid instead of a Newtonian one. Copyright © 2015 John Wiley & Sons, Ltd.     

Mobility‐dependent bifurcations in capillarity‐driven two‐phase fluid systems by using a lattice Boltzmann phase‐field model

Bifurcations in capillarity‐driven two‐phase fluid systems, due to different mobilities in phase‐field models for such systems, are studied by using a lattice Boltzmann method (LBM). Specifically, two‐dimensional (2D) and three‐dimensional (3D) droplets on a flat wall with given wettability variations are investigated. It is found that the mobility controls the rate of diffusive relaxation of the phase field from non‐equilibrium toward equilibrium, and similar to previous findings on mechanically driven two‐phase systems, the mobility is closely related to the contact line velocity. For the cases investigated, different mobilities across a critical value result in fundamentally different system evolution routes and final stable equilibrium states. These results may provide some implications for phase‐field study of droplet manipulations by surface wettability adjustments in microfluidics. Copyright © 2008 John Wiley & Sons, Ltd.     

Unified one‐fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the immersed structural potential method (ISPM)

In this paper, we present a two‐dimensional computational framework for the simulation of fluid‐structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single‐phase flows. First, a variation of classical immersed techniques, pioneered with the immersed boundary method (IBM), is presented by rearranging the governing equations, which define the behaviour of the multiple physics involved. The formulation is compatible with the “one‐fluid” formulation for two‐phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the immersed structural potential method developed by the authors, by adding a level set–based method for the capturing of the fluid‐fluid interfaces and an interface Lagrangian‐based meshless technique for the tracking of the fluid‐structure interface. The spatial discretisation is based on the standard marker‐and‐cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second‐order time integrator, and a fixed‐point iterative scheme. The paper presents a wide d range of two‐dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.     

A simulation of free surface waves for incompressible two‐phase flows using a curvilinear level set formulation

A level set formulation in a generalized curvilinear coordinate is developed to simulate the free surface waves generated by moving bodies or the sloshing of fluid in a container. The Reynolds‐averaged Navier–Stokes (RANS) equations are modified to account for variable density and viscosity in two‐phase (i.e. water–air) fluid flow systems. A local level set method is used to update the level set function and a least square technique adopted to re‐initialize it at each time step. To assess the developed algorithm and its versatility, a selection of different fluid–structure interaction problems are examined, i.e. an oscillating flow in a two‐dimensional square tank, a breaking dam involving different density fluids, sloshing in a two‐dimensional rectangular tank and a Wigley ship hull travelling in calm water. Copyright © 2005 John Wiley & Sons, Ltd.     

Simulation of two‐phase flow with moving immersed boundaries

A two‐dimensional multi‐phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier–Stokes equation coupled with a phase‐field model based on van der Waals' free energy density and the Cahn–Hilliard equation. A new phase‐field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas–Washburn theory and Stefan's problem. The proposed model may be used for multi‐phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium. Copyright © 2010 John Wiley & Sons, Ltd.     

Extension of a high‐resolution scheme to 1D liquid–gas flow

This paper presents the extension of a high‐resolution conservative scheme to the one‐dimensional one‐pressure six‐equation two‐fluid flow model. Only mixtures of water and air have been considered in this study, both fluids have been characterized using simple equations of state, namely stiffened gas for the liquid phase and perfect gas for the gas phase. The resulting scheme is explicit and first‐order accurate in space and time. A second‐order version of the scheme has also been derived using the MUSCL strategy and slope limiters. Some numerical results show the good capabilities of this type of schemes in the solution of discontinuities in two‐fluid flow problems, all of them are based on water/air numerical benchmarks widely used in the two‐phase flow literature. Copyright © 2005 John Wiley & Sons, Ltd.     

Simulation of sharp gas–liquid interface using VOF method and adaptive grid local refinement around the interface

The volume of fluid (VOF) method is used to perform two‐phase simulations (gas–liquid). The governing Navier–Stokes conservation equations of the flow field are numerically solved on two‐dimensional axisymmetric or three‐dimensional unstructured grids, using Cartesian velocity components, following the finite volume approximation and a pressure correction method. A new method of adaptive grid local refinement is developed in order to enhance the accuracy of the predictions, to capture the sharp gas–liquid interface and to speed up the calculations. Results are compared with experimental measurements in order to assess the efficiency of the method. Copyright © 2004 John Wiley & Sons, Ltd.     

Theoretical analysis for achieving high‐order spatial accuracy in Lagrangian/Eulerian source terms

In a fully coupled Lagrangian/Eulerian two‐phase calculation, the source terms from computational particles must be agglomerated to nearby gas‐phase nodes. Existing methods are capable of accomplishing this particle‐to‐gas coupling with second‐order accuracy. However, higher‐order methods would be useful for applications such as two‐phase direct numerical simulation and large eddy simulation. A theoretical basis is provided for producing high spatial accuracy in particle‐to‐gas source terms with low computational cost. The present work derives fourth‐ and sixth‐order accurate methods, and the procedure for even higher accuracy is discussed. The theory is also expanded to include two‐ and three‐dimensional calculations. One‐ and two‐dimensional tests are used to demonstrate the convergence of this method and to highlight problems with statistical noise. Finally, the potential for application in computational fluid dynamics codes is discussed. It is concluded that high‐order kernels have practical benefits only under limited ranges of statistical and spatial resolution. Additionally, convergence demonstrations with full CFD codes will be extremely difficult due to the worsening of statistical errors with increasing mesh resolution. Copyright © 2006 John Wiley & Sons, Ltd.