The robustness issue on multigrid schemes applied to the Navier–Stokes equations for laminar and turbulent,incompressible and compressible flows

The paper's leitmotiv is condensed in one word: robustness. This is a real hindrance for the successful implementation of any multigrid scheme for solving the Navier–Stokes set of equations. In this paper, many hints are given to improve this issue. Instead of looking for the best possible speed‐up rate for a particular set of problems, at a given regime and in a given condition, the authors propose some ideas pursuing reasonable speed‐up rates in any situation. In a previous paper, the authors presented a multigrid method for solving the incompressible turbulent RANS equations, with particular care in the robustness and flexibility of the solution scheme. Here, these concepts are further developed and extended to compressible laminar and turbulent flows. This goal is achieved by introducing a non‐linear multigrid scheme for compressible laminar (NS equations) and turbulent flow (RANS equations), taking benefit of a convenient master–slave implementation strategy. Copyright © 2004 John Wiley & Sons, Ltd.     

非线性流固耦合问题的ALE分步有限元数值方法

推导了一种基于ALE（Arbitrary Lagrangian-Eulerian,即任意的拉格朗日-欧拉）描述下的带有自由液面不可压液体与运动结构非线性耦合问题的一种有限元数值计算方法,在时间域上采用分步格式计算,这种方法与混合插值方法比较其优点是速度和压力可使用同阶线性插值,给数值计算带来很大方便,将所得到的方法应用到结构与TLD（调谐式（液体阻尼器）装置之间的耦合问题,数值计算结果验证了本文所推导的方法。     

薄板坯连铸结晶器中钢液三维流动的数值模拟

采用高 Re数的紊流 K- ε两方程模型 ,且结合壁面函数法对薄板坯连铸结晶器中钢液的紊流流动进行了有限元数值模拟。在数值模拟中 ,考虑了凝固壳厚度分布对流场的影响。在掌握了结晶器内紊流粘性系数分布规律的基础上 ,将流动域在空间进行了分区 ,采用分区选定有效粘性系数的当量层流模型数值模拟了三维紊流流动 ,结果表明 ,当量层流模型可有效的获得与原紊流时均场基本一致的结果 ,但计算效率显著提高 ,为今后工程上计算薄板坯结晶器中的三维流动和考虑流动影响的凝固过程分析提供了实用的方法 ,计算结果也有助于人们对薄板坯连铸结晶器中钢液三维紊流流动特点和与流动有关的板坯质量等问题的理解     

Numerical residual elimination method of finite differential equations

In this paper,a new elimination of finite differential equations has been discussed.It applies the numerical direct iteration to obtain the residual equations,in which the number of unknowns has been reduced greatly.The solution process is simple and efficient,and the solution is exact     

A projection scheme for incompressible multiphase flow using adaptive Eulerian grid

This paper presents a finite element method for incompressible multiphase flows with capillary interfaces based on a (formally) second‐order projection scheme. The discretization is on a fixed Eulerian grid. The fluid phases are identified and advected using a level set function. The grid is temporarily adapted around the interfaces in order to maintain optimal interpolations accounting for the pressure jump and the discontinuity of the normal velocity derivatives. The least‐squares method for computing the curvature is used, combined with piecewise linear approximation to the interface. The time integration is based on a formally second order splitting scheme. The convection substep is integrated over an Eulerian grid using an explicit scheme. The remaining generalized Stokes problem is solved by means of a formally second order pressure‐stabilized projection scheme. The pressure boundary condition on the free interface is imposed in a strong form (pointwise) at the pressure‐computation substep. This allows capturing significant pressure jumps across the interface without creating spurious instabilities. This method is simple and efficient, as demonstrated by the numerical experiments on a wide range of free‐surface problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Simulation of free-surface flows by a finite element interface capturing technique

Transient free-surface (FS) flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by the positive values of the level set function, the gaseous phase by negative ones, and the FS by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier–Stokes stage, (ii) an advection stage for the transport of the level set function and (iii) a bounded reinitialisation with continuous penalisation stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalisation stage, is evaluated in three typical two- and three-dimensional problems.     

A deforming-mesh finite-element approach applied to the large-translation and free-surface scenario of fused deposition modeling

A numerical study of the fused deposition modeling (FDM) process using a boundary-conforming free-surface finite element approach is performed. Due to the complexity of the FDM process, among all of its parts, we focus on the deposition and spreading of an individual filament. The polymer behavior, that is, the shear rate dependent and temperature-dependent viscosity, is included by the Cross-WLF viscosity model. The moving domain is addressed by the virtual region mesh update method, which, in the present article, is extended to free-surface problems. The particularity of dividing the mesh domain into an activated and a deactivated domain makes it possible to handle large translatory mesh deformation. In this work, we make use of the level of detail offered by a boundary-conforming approach regarding both topology accuracy and the imposition of boundary conditions in order to study the deposition of a single filament at a small scale. Parameters with a direct impact on the mechanical properties of the final object can be straightforwardly computed by a boundary-conforming approach, for instance, the cross-section, the contact area, the temperature distribution, and the heat fluxes over the surfaces. The presented approach is validated by a two-dimensional benchmark test case before the numerical results of the three-dimensional simulation of the filament deposition are shown.     

Numerical Fluid Flow Analysis for Aerodynamic Response Characteristics of Tandem Circular Cylinders

The aerodynamic characteristics of tandem cables of cable-stayed bridges have become an increasingly serious problem with increments in span length. In order to reduce the construction cost and maintenance of cables, tandem cables have been adopted for cable-stayed bridges. These cables, however, have aerodynamic response characteristics such as wake-galloping. Therefore, a method to suppress wake-galloping in tandem cables is required. The purpose of this study is to investigate the characteristics of the wake-galloping phenomenon of tandem cables of cable-stayed bridges using numerical fluid flow analysis. The flow around the oscillating tandem circular cylinders modeled on tandem cables is calculated. The flow field is treated as an incompressible viscous flow. The Arbitrary Lagrangian-Eulerian (ALE) method is employed to solve the flow field around the cylinders, and the three-step Taylor-Galerkin method, which is based on a fractional step finite element method, is adopted for discretization.     

薄膜-基体型磁致伸缩微致动器的数值模拟

磁致伸缩薄膜是一种性能优异的微驱动元件。本文针对磁致伸缩薄膜一基体结构中薄膜磁致伸缩系数与层合结构变形之间关系的问题，从经典层合板理论的角度导出了其基本方程，并在此基础上对基体远厚于薄膜的情形采用非层合板理论进行了简化。通过比较非层合板理论和层合板理论下的薄膜一基体结构变形的有限元结果，讨论了有关几何参数和物理参数的影响，给出了用非层合板理论近似处理薄膜一基体型磁致伸缩微致动器的适用条件。     

含有序孔洞的多孔氧化铝薄膜的力学性能测量和数值模拟

高纯铝箔在特定的溶液下经过电化学阳极氧化腐蚀,可在其表面生成一层多孔的非晶氧化铝层,其孔径分布非常均匀,孔大致呈六方密排布。由于此类薄膜具有规则的纳米级孔径,大的比表面积,良好的自组织排列性,所以其日益受到人们的关注。然而,到目前为止,对于此类薄膜力学性能的研究还很少,所以在一定程度上限制其功能的开发和应用。为了获得此类多孔膜的弹性常数,本文首先由实验出发,通过光力学检测(双光束散斑干涉)的方法得到薄膜拉伸时的整体表观弹性模量。然后对薄膜建立二维有限元模型,运用均匀化理论反推出其基体(无孔结构)的弹性模量,同时考察了不同的基体泊松比对模型整体表观模量的影响,并且用一般有限元方法验证了沿特定方向拉伸时均匀化模型计算的有效性。     

Simulation of Coupled Viscous and Porous Flow Problems

Theoretical and numerical formulations are presented for the conjugate problem involving incompressible flow and flow in a saturated porous medium. The major focus of the work is the development of a generally applicable finite element method for the simulation of both fixed interface and evolving porous interface problems. The available alternatives for coupling Darcy and non-Darcy models to the Navier-Stokes equations have been studied and evaluated in a mixed finite element framework. Questions regarding convergence of the finite element method for porous flow models have been addressed. Numerical experiments on simple flow geometries have revealed the shortcomings of both the Darcy and Brinkman models. Application of the more realistic models to practical, multidimensional, flow studies has also been demonstrated.     

Numerical simulation of flow‐induced noise using LES/SAS and Lighthill's acoustic analogy

We present a finite element (FE) formulation of Lighthill's acoustic analogy for the hybrid computation of noise generated by turbulent flows. In the present approach, the flow field is computed using large eddy simulation and scale adaptive simulation turbulence models. The acoustic propagation is obtained by solving the variational formulation of Lighthill's acoustic analogy with the FE method. In order to preserve the acoustic energy, we compute the inhomogeneous part of Lighthill's wave equation by applying the FE formulation on the fine flow grid. The resulting acoustic nodal loads are then conservatively interpolated to the coarser acoustic grid. Subsequently, the radiated acoustic field can be solved in both time and frequency domains. In the latter case, an enhanced perfectly matched layer technique is employed, allowing one to truncate the computational domain in the acoustic near field, without compromising the numerical solution. Our hybrid approach is validated by comparing the numerical results of the acoustic field induced by a corotating vortex pair with the corresponding analytical solution. To demonstrate the applicability of our scheme, we present full 3D numerical results for the computed acoustic field generated by the turbulent flow around square cylinder geometries. The sound pressure levels obtained compare well with measured values. Copyright © 2009 John Wiley & Sons, Ltd.     

A 3D finite element ALE method using an approximate Riemann solution

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann‐like problem. Two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well‐known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

大变形中摩擦接触问题的数值模拟及应用

大变形的摩擦接触是复杂的非线性问题 ,本文介绍了一种处理摩擦接触问题的数值方法。采用接触单元技术模拟接触界面 ,基于弹塑性理论形式的非经典Coulomb摩擦定律及罚函数方法建立了摩擦接触的增量本构关系。结合大变形的增量分析格式给出了积分摩擦接触本构方程的回映方法。这种处理摩擦接触问题的方法计算简单、使用方便。给出的计算实例及应用实例说明了方法的精度与稳定性     

高速列车紊态外流场的数值模拟研究

高速列车是近地运行的细长、庞大物体,它的空气绕流问题有其特殊性,本文以不可压缩粘性流体的Navier-Stokes方程和k-ε两方程紊流模型为基础,采用有限元方法求解了高速列车三维紊态外流场,针对有限元法应用于流场计算时常出现的问题,采用分离式解法,非对称矩阵一维变带宽压缩存储及带宽极小化等方法,最大限度地降低计算存储量;并采用罚函数法,集中质量矩阵,缩减积分法,带参数迭代法以及 引入松弛因子等技术,提出了一套用有限元法计算非线性问题的求解方法,提高了收敛速度的计算严谨,计算方法和计算结果对列车空气动力学的深入研究有一定的帮助。     

Numerical study around the corotational Maxwell model for the viscoelastic fluid flows

We present numerical results for the FEM (finite element method) presented in [Comput. Methods Appl. Mech. Engrg. 191 (2002) 5045–5065]. This method is devoted to the approximation of fluid flows obeying the Oldroyd model. A particularity of this method, is to take into account the purely viscoelastic case, the so-called Maxwell model, important in practice. Numerical results are given for a fluid flowing in an abrupt plane 4 to 1 contraction. We use the corotational Maxwell model as benchmark in the choice of our computations. Results are also given for the upper convected Maxwell model. Interesting effects appear on the velocity profile: a phenomenon of quasi slip at the downstream wall.     

A finite element model for the simulation of lost foam casting

In this paper, we present a numerical model to simulate the lost foam casting process. We introduce this particular casting first in order to capture the different physical processes in play during a casting. We briefly comment on the possible physical and numerical models used to envisage the numerical simulation. Next we present a model which aims to solve ‘part of’ the complexities of the casting, together with a simple energy budget that enables us to obtain an equation for the velocity of the metal front advance. Once the physical model is established we develop a finite element method to solve the governing equations. The numerical and physical methodologies are then validated through the solution of a two‐ and a three‐dimensional example. Finally, we discuss briefly some possible improvements of the numerical model in order to capture more physical phenomena. Copyright © 2004 John Wiley & Sons, Ltd.     

AN EULERIAN FINITE ELEMENT METHOD FOR TIME-DEPENDENT FREE SURFACE PROBLEMS IN HYDRODYNAMICS

A numerical method based on the finite element method is presented for simulating the two-dimensional transient motion of a viscous liquid with free surfaces. For ease of numerical treatment of the free surface expressed by a multiple-valued function, the marker particle method is employed. Numerous virtual particles are spread over all regions occupied by liquid. They move about on a fixed finite element mesh with the liquid velocity at their positions. These particles contribute nothing to the dynamics of the liquid and only serve as markers of liquid regions. The velocity field within liquid regions is calculated by solving the Navier– Stokes equations and the equation of continuity by the finite element method based on quadrilateral elements. A detailed discussion is given of the methodological problems arising in the implementation of the marker particle method on an unstructured finite element mesh and of the solutions to these problems. The proposed method is demonstrated on three sample problems: the broken dam problem, the impact of a falling liquid drop on a still liquid and the entry of a rigid block into water. Good agreement has been obtained in the comparison of the present numerical results with available experimental data.     

风口区空气流动的有限元模拟与实验研究

通风和空调出风口的射流特性主要取决于出风口截面之前的一段管道内的流动状况,研究送风口的射流偏转特性有重要实用价值.应用湍流大涡模拟技术结合Taylor-Galerkin有限单元法对工程中常见工况下的风口区管道内的三维流场进行了数值模拟和实验研究,数值计算结果与实验结果符合较好.表明湍流大涡模拟方法适合于边界形状复杂,存在各向异性的大尺度涡的内流情况,能可靠地预报风口区空气流动的射流偏转特性.     

Extension of the volume-of-fluid method for analysis of free surface viscous flow in an ideal gas

The volume-of-fluid (VOF) method is a simple and robust technique for simulating free surface flows with large deformations and intersecting free surfaces. Earlier implementations used Laplace's formula for the normal stress boundary condition at the interface between the liquid and vapour phases. We have expanded the interfacial boundary conditions to include the viscous component of the normal stress in the liquid phase and, in a limited manner, to allow the pressure in the vapour phase to vary. Included are sample computations that show the accuracy of added third-order-accurate differencing schemes for the convective terms in the Navier-Stokes equation (NSE), the viscous terms in the normal stress at the interface and the solution of potential flow in the vapour phase coupled with the solution of the NSE in the liquid phase. With these modifications we show that the VOF method can accurately predict the instability of a thin viscous sheet flowing through a stagnant vapour phase.