磨削加工中磨削区流场的数值分析

基于动压润滑理论,建立了浇注法方式下磨削区流场的光滑数学模型并利用多重网格法计算出了磨削区流场的动压力和流体速度;在光滑模型的基础上建立了考虑砂轮和工件表面粗糙度的粗糙模型并利用多重网格法得到该模型下的解.结果表明:粗糙模型得到的磨削加工区流体的动压力及流速曲线是不光滑的,但光滑模型和粗糙模型的解吻合较好.     

多重网格法求解微机械谐振器的挤压膜阻尼

针对求解MEMS挤压膜阻尼过程中存在的问题,采用了多重网格方法进行求解,与传统方法相比,应用于挤压膜中流体问题的求解具有收敛速度快,数值稳定性好的优点,求得了谐振器平板间的压力分布函数以及微谐振器的各个性能指标的值,研究了挤压膜中流体阻尼力的特性以及与谐振器件幅—频特性的关系。     

Variational multiscale methods for premixed combustion based on a progress-variable approach

In this study, novel computational techniques for the numerical simulation of premixed combustion based on a progress-variable formulation are proposed. Two new variational multiscale methods within a finite element framework are developed for the system of mass, momentum and progress-variable equations: a purely residual-based variational multiscale method and an algebraic variational multiscale-multigrid method. The proposed methods are tested for the numerical example case of a flame–vortex interaction using Arrhenius chemical kinetics. This actually laminar reactive flow problem may serve as a model problem for interactions of turbulent flows and (premixed) flames. The results obtained from this test case show that both methods are capable of accurately predicting the features expected during the progression of the flame–vortex interaction. The evolution of both a pocket of unburned gas and a secluded, drop-like structure, which detaches itself and moves upwards, are accurately predicted already for a relatively coarse discretization.     

Cascadic meshfree method for the elliptic Monge–Ampère equation

The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation, which originated in geometric surface theory and has been widely applied in dynamic meteorology, elasticity, geometric optics, image processing and others. The numerical solution of the elliptic Monge–Ampère equation has been a subject of increasing interest recently. In this paper, we design a cascadic algorithm which is meshfree. We first generate hierarchical scattered data sets. Then on each successive refinement levels, the Monge–Ampère equation can be solved by Kansa's method. We call this method as cascadic meshfree method (CMF). Different from cascadic multigrid method, CMF avoids tedious interpolation and is more easy for implementation and coding. Finally, numerical experiments confirm the efficiency and robustness of CMF method.     

渐开线直齿圆柱齿轮非稳态弹流润滑分析

综合考虑轮齿在不同啮合点处的曲率半径、卷吸速度、轮齿载荷随时间的变化，考虑压力对流体粘度和密度的影响．利用多重网格技术求得齿轮非稳态弹流润滑的完全数值解。分析了单双齿承载载荷谱和啮入冲击载荷对齿轮弹流润滑的影响。     

内燃机排气凸轮/挺柱机构的瞬态热弹性流体动力润滑研究

在对内燃机排气凸轮/挺柱机构进行运动学和动力学分析的基础上,采用多重网格法和多重网格积分技术对该摩擦副进行了热弹性流体动力润滑研究。结果表明:凸轮的一个旋转周期内的不同瞬时摩擦副的润滑状况存在显著的差别,压力、膜厚等相关参数都表现出剧烈的变化;最小膜厚和最高接触压力出现在凸轮挑尖处;卷吸速度为零的2个工作点之间是凸轮-挺柱润滑的危险区;摩擦造成的润滑油温升超过40℃。     

基于多重网格法的三维有限元程序设计

为了提高普通有限元方法在解决大型工程计算问题时的收敛性和准确性.文中在普通有限元方法的网格信息预处理过程和迭代求解过程中加入了多重网格方法的迭代方法和校正技术,使其与有限元方法有机地结合在一起,成功地构造了一种多重网格有限元法,并用FORTRAN95语言编写了面向对象的源代码SAFEM.数值验证表明,此方法收敛稳定、快速,且具有很高的精度,在加密网格与ABAQUS网格同样的条件下,能使其数值解与理论解的相对误差在1%之内,比ABAQUS解的相对误差稍低,而计算时间远远短于ABAQUS的求解时间,显示出极大的工程实用价值.     

结构动力响应分析的多重网格方法

提出了一种适合于有限元分析中求解结构动力响应的多重网格方法,该方法利用初始网格下的结果,通过双线性插值技术得到网格变化后新的近似位移向量,然后由多重网格迭代过程求解结构动力响应问题。在多重网格迭代的前光滑过程中,选择了共轭梯度法提高其收敛率;在粗网格校正过程中,给出了一种近似求解位移向量误差的方程;在后光滑过程中,选择了Jacobi松弛迭代提高解的光滑性。该方法将网格离散过程和数值求解过程结合在一起,建立了一个网格细分后结构动力响应问题的快速重分析方法,与传统有限元方法相比较,具有计算简便、迭代步骤少,运算时间短等特点,可以作为结构动力问题自适应有限元分析的一种十分有效的工具。同时,本文还给出了一种简单实用的时间步长划分的自适应方法。     

Multi‐time‐step and two‐scale domain decomposition method for non‐linear structural dynamics

In this paper we propose a method to improve the means of taking into account the specific time‐scale and space‐scale characteristics in time‐dependent non‐linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocities at the interfaces, which are modelled using a dual Schur formulation. For certain subdomains, in space, we adopt a two‐scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a refined scale and the part corresponding to large variation lengths on a coarse scale. For non‐linear problems, we propose an algorithm with a single iteration level to deal with both the non‐linear equilibrium and the two space scales thanks to a two‐grid method in which the relaxation steps are performed using a non‐linear, preconditioned conjugate gradient algorithm. Finally, we present an example which demonstrates the feasibility of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

Domain decomposition and multigrid solvers for flow simulation in porous media on distributed memory parallel processors

Realistic simulations of fluid flow in oil reservoirs have been proven to be computationally intensive. In this work, techniques for solving large sparse systems of linear equations that arise in simulating these processes are developed for parallel computers such as INTEL hypercubes iPSC/2 and iPSC/860. This solver is based on a combined multigrid and domain decomposition approach. The Algorithm uses line corrections solved using a multigrid method, line Jacobi and block incomplete domain decomposition as an overall preconditioner for a conjugate gradient-like acceleration method, ORTHOMIN (k). This is shown to be a factor of ten times faster on a 32-processor hypercube compared to widely used sequential solvers. Three test problems are used to validate the results which include implicit wells and faults: The first is based on highly heterogeneous two-phase flow, the second on the SPE Third Comparative Solution and the third on real production compositional data.