自适应多重网格有限元网格生成器研制

基于协调三角形剖分算法、分子表数据结构和Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ误差估计方法，本文研制出适用于自适应多重网格有限元的网格生成器。该网格生成器可对复杂的区域进行自适应加密。当荷载作用边界随时间变化及在动力荷载作用下，网格生成器可退化与再加密网格。     

一种适用于板料成形过程分析的自适应有限元方法

本文主要讨论在板料成形过程的动态显式有限元分析中,有限元网格的丙分割技术。单元为四节点壳单元,板料的材料特性假定满足Ｈｉｌｌ各向异性的弹塑性准则,采用自适应ｈ－方案,通过细化和聚合单元调整网格的疏密,模具被假定为由刚性小平面组成,与同一单元的节点发生接触处的模具表面的法线之间的夹角作为单元再分的判据。通过对方表盒冲压成形过程的计算,说明该方法是有效的。     

An adaptive finite element method for forced convection

This paper presents an adaptive finite element method to solve forced convective heat transfer. Solutions are obtained in primitive variables using a high-order finite element approximation on unstructured grids. Two general-purpose error estimators are developed to analyse finite element solutions and to determine the characteristics of an improved mesh which is adaptively regenerated by the advancing front method. The adaptive methodology is validated on a problem with a known analytical solution. The methodology is then applied to heat transfer predictions for two cases of practical interest. Predictions of the Nusselt number compare well with measurements and constitute an improvement over previous results. © 1997 John Wiley & Sons, Ltd.     

The three-dimensional prolonged adaptive unstructured finite element multigrid method for the Navier–Stokes equations

This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier–Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill-in preconditioner. The test problem considered is the three-dimensional driven cavity flow. © 1997 John Wiley & Sons, Ltd.     

Discontinuity-capturing finite element computation of unsteady flow with adaptive unstructured mesh

A discontinuity-capturing scheme of finite element method (FEM) is proposed. The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows, which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular, a new testing variable, i.e., the disturbed kinetic energyE, is suggested and used in the adaptive mesh computation, which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number. Based on several calculated examples, this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows. The project supported by the National Natural Science Foundation of China (10125210), the Hundred-Talent Programme of the Chinese Academy of Sciences and the Innovation Project of the Chinese Academy of Sciences (KJCX-SW-L04, KJCX2-SW-L2)     

A multimesh adaptive scheme for air quality modeling with the finite element method

A multimesh adaptive scheme for convection–diffusion–reaction problems for a large number of components is presented. The problem is solved by splitting transport and reaction processes. This way, the evaluation of the nonreactive part for each component and the reaction at each node constitute independent tasks. This allows to discretize each component of the solution on a distinct computational mesh, adapted on the basis of its error indicator. The standard single‐mesh strategy is used for comparison. Simulations of a point emission in a 3D domain are presented. Low remeshing periods of the adaptive scheme are found to be optimal, in terms of computational cost and accuracy, for the nonreactive problem. Examples with several reaction terms, with an increase of the complexity, are then presented. Results show that the accuracy of single‐mesh and multimesh strategies are similar. Instead, the computational cost of the multimesh strategy is lower than the single‐mesh in the majority of the examples; this process is controlled by the stiff behavior of the reactive term. The problem size of the multimesh scheme is much lower, and therefore, larger spatial discretizations can be simulated for a given available memory. The efficiency of the multimesh strategy increases with the number of species and the number of species that develop a plume. Finally, an example of a punctual emission considering realistic values of the initial concentrations and using the Community Multiscale Air Quality‐CBO5 reaction model, which involves 62 components, is presented; the small‐scale structure of the different nitrogen components near the emitter is captured. Copyright © 2013 John Wiley & Sons, Ltd.     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

This paper introduces an adaptive finite element method (AFEM) using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.     

近场动力学与有限元的混合建模方法

综述了近场动力学与有限元混合建模方法的研究进展,阐明了各种混合建模方法的基本原理与特点,并重点介绍本课题组在近场动力学与有限元方法混合建模方面的研究工作。现有近场动力学与有限元混合建模方法包括位移协调约束、力耦合、混合函数方法以及子模型方法等,除子模型方法外,都可归结为并行式多尺度分析方法,其基本思想是将计算结构划分为近场动力学子域、有限元子域以及两者的交界区域(或重叠区域、或界面单元、或过渡区域)。子模型方法可归结为显-显分析方法,先采用显式有限元进行整体分析,后采用近场动力学方法对重点区域进行分析。混合建模方法需要着重提高交界区域的计算精度,并且消除虚假力和虚假应力波问题。提出了通过力耦合的近场动力学与有限元混合建模的隐式分析方法,该方法不再设置重叠区,通过杆单元连接近场动力学子域与有限元子域,其中界面上的有限元结点不仅与其所在单元的其他结点发生作用,还通过杆单元与以其为圆心、一定半径的圆域内的其他物质点相互作用。研究表明,本文提出的混合模型和求解方法既能有效解决裂纹扩展等不连续问题,又可提高计算效率,为工程结构破坏问题的计算分析提供一种有效方法。