A Voronoi‐based ALE solver for the calculation of incompressible flow on deforming unstructured meshes

An Arbitrary Lagrangian–Eulerian method for the calculation of incompressible Navier–Stokes equations in deforming geometries is described. The mesh node connectivity is defined by a Delaunay triangulation of the nodes, whereas the discretized equations are solved using finite volumes defined by the Voronoi dual of the triangulation. For prescribed boundary motion, an automatic node motion algorithm provides smooth motion of the interior nodes. Changes in the connectivity of the nodes are made through the use of local transformations to maintain the mesh as Delaunay. This allows the nodes and their associated Voronoi finite volumes to migrate through the domain in a free manner, without compromising the quality of the mesh. An MAC finite volume solver is applied on the Voronoi dual using a cell‐centred non‐staggered formulation, with cell‐face velocities being calculated by the Rhie–Chow momentum interpolation. Advective fluxes are approximated with the third‐order QUICK differencing scheme. The solver is demonstrated via its application to a driven cavity flow, and the flow about flapping aerofoil geometries. Copyright © 2010 John Wiley & Sons, Ltd.     

Cahn–Hilliard modeling of particles suspended in two‐phase flows

In this paper, we present a model for the dynamics of particles suspended in two‐phase flows by coupling the Cahn–Hilliard theory with the extended finite element method (XFEM). In the Cahn–Hilliard model the interface is considered to have a small but finite thickness, which circumvents explicit tracking of the interface. For the direct numerical simulation of particle‐suspended flows, we incorporate an XFEM, in which the particle domain is decoupled from the fluid domain. To cope with the movement of the particles, a temporary ALE scheme is used for the mapping of field variables at the previous time levels onto the computational mesh at the current time level. By combining the Cahn–Hilliard model with the XFEM, the particle motion at an interface can be simulated on a fixed Eulerian mesh without any need of re‐meshing. The model is general, but to demonstrate and validate the technique, here the dynamics of a single particle at a fluid–fluid interface is studied. First, we apply a small disturbance on a particle resting at an interface between two fluids, and investigate the particle movement towards its equilibrium position. In particular, we are interested in the effect of interfacial thickness, surface tension, particle size and viscosity ratio of two fluids on the particle movement towards its equilibrium position. Finally, we show the movement of a particle passing through multiple layers of fluids. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive Lagrangian–Eulerian computation of propagation and rupture of a liquid plug in a tube

Liquid plug propagation and rupture occurring in lung airways can have a detrimental effect on epithelial cells. In this study, a numerical simulation of a liquid plug in an infinite tube is conducted using an Eulerian–Lagrangian approach and the continuous interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information about the interface mesh. Results prior to the rupture are in reasonable agreement with the study of Fujioka et al. in which a Lagrangian method is used. For unity non‐dimensional pressure drop and a Laplace number of 1000, rupture time is shown to be delayed as the initial precursor film thickness increases and rupture is not expected for thicknesses larger than 0.10 of tube radius. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage. The peak values of those stresses increase as the initial precursor film thickness is reduced. After rupture, the peaks in mechanical stresses decrease in magnitude as the plug vanishes and the flow approaches a fully developed behavior. Increasing initial pressure drop is shown to linearly increase maximum variations in wall pressure and shear stress. Decreasing the pressure drop and increasing the Laplace number appear to delay rupture because it takes longer for a fluid with large inertial forces to respond to the small pressure drop. Copyright © 2010 John Wiley & Sons, Ltd.     

A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces

Discontinuous Galerkin (DG) methods have been well established for single-material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed DG (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. A second-order DG(P₁) method and a third-order least-squares based rDG(P₁P₂) are used to discretize this system in space, and a third-order total variation diminishing (TVD) Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented and is verified by numerical test problems. Furthermore, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are, indeed, the second- and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-material system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multidimensional high-order rDG method for multi-material hydrodynamics.     

Validation of a fluid–structure interaction model for a bileaflet mechanical heart valve

A fluid-structure interaction (FSI) model for heart valve simulation is presented. In a partitioned framework, separate fluid and structure solvers are weakly coupled, which in combination with the use of artificial compressibility in the fluid solver, leads to a stable and efficient approach. An Arbitrary Lagrangian Eulerian formulation is employed in the fluid solver to permit the accurate calculation of shear stresses next to the valve boundary. The mesh quality is maintained through a combination of smoothing and local remeshing in 3D. The FSI algorithm is validated on experiments of an idealised quasi-2D mechanical heart valve, and the efficiency of the remeshing approach is demonstrated on a realistic 3D heart-valve geometry.     

复合材料尖劈和接头端部奇性场的反平面问题研究

提出了一个基于位移的分析尖劈端部奇性位移场和应力场反平面问题的非协调元特征法．该方法与过去原有求解裂纹尖端近似场的有限元特征法有几点不同：(1)导出虚功原理的出发点为二维扇区的散度原理;(2)有限元的单元形式为非协调元;(3)尖劈端部邻域内的位移场假定没有采用奇异变换技术．运用该方法给出了求解正交各向异性复合材料尖劈端部附近奇性应力指数、奇性位移和应力角分布函数的算例．计算结果表明,该方法较原来的有限元特征法所用的单元少而且精度高．     

多物质流体动力学方法与结构动力学方法结合的流固耦合计算技术

建立一种基于重叠网格空间覆盖判断的流固耦合计算技术,把流场计算的Euler多物质流体动力学计算过程和Lagrange结构动力学计算过程相结合以描述流固间的相互作用.介绍该计算技术的具体实现过程,讨论提高几何判断效率、避免耦合遗漏、流固计算时间步协调等处理技术.应用建立的流固耦合计算程序模拟爆炸容器中爆炸流场对容器内部结构、容器壳体的作用过程.计算结果表明其可以反映流场发展过程、流场结构相互作用和结构的运动变形和破坏过程.     

基于MOF界面重构的多物质ALE方法

提出一种基于MOF(Moment-of-Fluid)界面重构的多物质ALE(Arbitrary Lagrangian-Eulerian)方法.流体力学方程组采用相容有限元方法进行空间离散.提出一种新的二维子网格力学模型,用来计算混合网格中的物理量经过一个拉氏步后发生的变化,混合网格内的界面重构采用MOF方法.提出一种精确积分守恒重映方法.给出数值算例,如空气和水的Riemann问题,Dukowicz问题,水中强激波与空气泡相互作用问题等.结果表明,方法具有较高的精度,能够处理物质界面和网格的大变形问题.     

All Eulerian method of computing elastic response of explosively pressurised metal tube

We present an all Eulerian approach to simulate the elastic response of a metal tube loaded explosively by a gaseous detonation. The high strain rate deformation of the metal tube subjected to high explosive detonation is mathematically described by hyperbolic processes where the characteristics of existing wave motions were correlated with the local particle velocities through the speed of sound in the metal. This is a favourable case for the hydrocode which is based on a compressible gas dynamics solver and for simulating a high strain rate and dominantly plastic response of a material subject to an explosive loading. The hydrocodes fall substantially short of predicting elastic motion without the plastic flow of the confining material, for relatively minor pressure loadings due to a gaseous explosion as opposed to a high explosive detonation of a charged tube. The corresponding loading pressure due to gaseous explosion is a few orders of magnitude lower than those resulting from high explosive loadings. Utilising a hydrocode designed to handle the reactive process leading to a plastic flow of the confining materials is of great interest and a significant challenge. The new technique, based on the Eulerian framework, preserves the feature of a Lagrangian code while utilising all the benefits of an Eulerian solver that uses fixed grids with the level-sets for defining the multi-material interfaces. The hybrid particle level-set algorithm is combined with a hydrodynamic solver that adds an elasticity correction when handling the structural response while the overall scheme remained hyperbolic during the entire reactive flow. Several unseen dynamics of detonation flow associated with the elastically loaded tube of finite thickness are reported by using the present method for analysing the highly pressurised vessel.     

串列双圆柱绕流下游圆柱两自由度涡致振动研究

数值研究了串列双圆柱绕流下游圆柱两自由度涡致振动问题，研究发现：(1) 双自由度的圆柱振幅峰值及出现振峰的频率比都比单自由度的大；(2) 尾流圆柱中的升力远大于均匀来流的，而阻力却相反；(3) 下游圆柱的位移响应对于频率比的变化没有均匀来流中的"敏感"；(4) 尾流中，在频率比1.16和0.87之间，出现了明显的"拍"现象，即圆柱的振幅响应包含不同的频率，而在均匀来流中，并无明显的"拍"现象. 采用ALE方法，计算网格采用H-O非交错网格系统，结合分块耦合方法. N-S方程的对流项和扩散项分别采用三阶迎风紧致格式和四阶中心紧致格式离散. 圆柱振动采用弹簧柱体阻尼器模型，柱体的振动方程采用龙格-库塔法求解. 通过模拟柱体和流体之间的非线性耦合作用，成功地捕捉到了"拍"和"相位开关"等现象.