自适应网格加密和多重网格求解严重病态方程

本文探讨用自适应网格加密技术结合多重网格法求解由有限元离散导致的病态方程。计算结果表明；自适应多重网格有限元法是求解严重病态方程珠有效方法。     

用混合网格及各向异性多重网格法求解三维可压紊流流动

采用混合网格求解紊流Navier Stokes方程。在物面附近采用柱状网格 ,其他区域则采用完全非结构网格。方程的求解采用Jamson的有限体积法 ,紊流模型采用两层Baldwin Lomax代数紊流模型。用各向异性多重网格法来加速解的收敛。数值算例表明 ,用混合网格及各向异性多重网格求解紊流流动是非常有效的     

考虑磁头表面高度不连续性气膜润滑的数值模拟与有效算法

随着磁头滑块的飞行高度不断降低,给气体润滑方程的数值求解带来了诸如计算时间过长、甚至计算发散等方面的问题。为了获得1Tbit/in2的存储密度,磁头滑块尾部的最小飞行高度接近1.5nm。本文基于作者提出的修正气膜润滑方程的线性流率(LFR)模型,考虑磁头滑块表面高度的不连续性,建立了基于有限体积法的气膜润滑方程离散格式,并把网格自适应技术与多重网格法应用到离散方程的迭代算法中,发展了可模拟最小飞行高度为0.5nm时磁头滑块压力分布的数值模拟方法与有效算法。文中以一个具有复杂表面形状的磁头滑块为例,检验了计算方法与算法的有效性。数值结果表明:在磁头滑块最小飞行高度较低时,必须要考虑滑块表面高度的不连续性,否则就得不到收敛的数值计算结果;与FK-Boltzmann模型相比,LFR模型具有较高的计算效率,采用网格自适应技术与多重网格法能有效地提高求解气膜润滑方程的计算效率。     

多重网格法求解轴流压气机内部流场

提出了一种能够与显式时间推进法、有限体积差分格式、粘性体积力法有效地配合使用的有效地配合使用的多重网格法来解轴流压气机内部流场。作者对美国NASA37^#跨音速轴流压气机转子内部流场的数值计算表明,多重网格法的计算结果与试验结果吻合, 同时该多重网格法的收敛速度比不用多重网格法加快了1．5倍。     

自适应无网格法在生物涂层接触问题中的应用

自适应无网格法是针对有限元法无法求解或者不易求解的复杂问题,利用无网格法节点排布灵活、易于增删节点、便于自适应分析等优点发展起来的. 在对自适应无网格法理论基础和发展进行总结基础上,采用基于应变能梯度的自适应无网格—— 有限元耦合方法,对等离子喷涂制备的HA 生物涂层材料的无摩擦接触问题进行分析,对制备的两种不同厚度的生物涂层材料进行求解,分别给出了von Mises 应力分布云图. 结果表明,自适应无网格法能较好地应用于生物涂层接触问题中.     

多重网格法与Newton-Raphson法耦合求线弹流数值解

利用多重网格算法,在最粗网格上,采用Newton-Raphson迭代法模式精解线接触弹流非线性方程组,充分利用了多重网格法与Newton-Raphson法各自的优点,计算实践表明,求解弹流问题的数值解过程在收敛与稳定性方面均有较大改善,且有相当宽的载荷参数适用范围。     

基于Kriging插值无网格法求解轴对称弹性力学问题

基于Kriging插值无网格法,提出了实际应用中复杂轴对称弹性力学问题求解的一条新途径.Kriging插值无网格法是一种新型的无网格法,该方法构造的形函数满足Kronecker delta函数性质,可以直接施加本质边界条件.采用Kriging插值无网格法分析轴对称问题,得到了轴对称问题的无网格离散方程,并编制了相应的计算程序.通过厚壁圆筒的静力学和动力学分析,对所提方法进行了检验.数值算例结果表明,提出的方法对求解轴对称弹性力学问题是行之有效的.     

不可压缩流场多体运动问题的两种数值解法

不可压缩流场中多体运动的数值模拟是计算流体动力学的前沿课题,目前可以求解此问题的两种高精度方法是重叠网格法和移动网格法。本文详细讨论了两种方法的理论基础,典型算法的实现过程,并采用两种方法对单圆柱和多圆柱运动问题进行了数值试验。通过分析比较,本文认为重叠网格法计算效率高于移动网格法,重叠网格法比移动网格法更适合于求解物体大位移运动问题,尤其当计算区域几何形状复杂时重叠网格法的优势更加明显。     

配点型无网格法理论和研究进展

有限元法是当前工程科学领域应用最广泛的数值计算方法之一,但是其在求解极端大变形、高速碰撞等一些复杂问题时,容易出现网格畸变和网格敏感性,从而导致计算结果精度低和不收敛的问题.为了避免网格带来的问题,出现并兴起了各种无网格法.无网格法不仅建模简便,而且收敛速度更快、计算精度更高,可用于求解有限元等网格类方法难以求解乃至尚未触及的问题.本文首先阐述了无网格法的分类以及具有代表性的方法.目前限制无网格法发展的主要问题是效率偏低.伽辽金型无网格法效率较低,而配点型无网格法效率较高,在复杂问题的高效高精度数值模拟中具有更大潜力.因此本文详细介绍了配点型无网格法的起源和研究进展,归纳了其常用的近似函数和离散方法,最后对无网格法的发展做出了总结和展望.无网格法的研究和改进,为复杂问题的高效高精度数值模拟开辟了新的途径.     

利用无网格法进行几何非线性热固耦合柔性机构拓扑优化设计

将无网格伽辽金法引入到拓扑优化中,利用其进行了几何非线性热固耦合柔性机构的优化设计研究.利用无网格法离散和求解了热固耦合场的控制方程.基于SIMP模型和无网格法,建立了柔性机构的优化模型,利用MMA方法求解.研究了基于无网格法的伴随敏度分析方法,并提出了解决拓扑结构出现不连续散乱点同题的敏度过滤方法.求解经典算例,表明本文方法的正确性和有效性.     

Multigrid flow solutions in complex two-dimensional geometries

A finite difference solution algorithm is described for use on two-dimensional curvilinear meshes generated by the solution of the transformed Laplace equation. The efficiency of the algorithm is improved through the use of a full approximation scheme (FAS) multigrid algorithm using an extended pressure correction scheme as smoother. The multigrid algorithm is implemented as a fixed V-cycle through the grid levels with a constant number of sweeps being performed at each grid level. The accuracy and efficiency of the numerical code are validated using comparisons of the flow over two backward step configurations. Results show close agreement with previous numerical predictions and experimental data. Using a standard Cartesian co-ordinate flow solver, the multigrid efficiency obtainable in a rectangular system is shown to be reproducible in two-dimensional body-fitted curvilinear co-ordinates. Comparisons with a standard one-grid method show the multigrid method, on curvilinear meshes, to give reductions in CPU time of up to 93%.     

Calculation of three‐dimensional turbulent flow with a finite volume multigrid method

A numerical method for the efficient calculation of three‐dimensional incompressible turbulent flow in curvilinear co‐ordinates is presented. The mathematical model consists of the Reynolds averaged Navier–Stokes equations and the k–ε turbulence model. The numerical method is based on the SIMPLE pressure‐correction algorithm with finite volume discretization in curvilinear co‐ordinates. To accelerate the convergence of the solution method a full approximation scheme‐full multigrid (FAS‐FMG) method is utilized. The solution of the k–ε transport equations is embedded in the multigrid iteration. The improved convergence characteristic of the multigrid method is demonstrated by means of several calculations of three‐dimensional flow cases. Copyright © 1999 John Wiley & Sons, Ltd.     

A finite volume unstructured multigrid method for efficient computation of unsteady incompressible viscous flows

An unstructured non‐nested multigrid method is presented for efficient simulation of unsteady incompressible Navier–Stokes flows. The Navier–Stokes solver is based on the artificial compressibility approach and a higher‐order characteristics‐based finite‐volume scheme on unstructured grids. Unsteady flow is calculated with an implicit dual time stepping scheme. For efficient computation of unsteady viscous flows over complex geometries, an unstructured multigrid method is developed to speed up the convergence rate of the dual time stepping calculation. The multigrid method is used to simulate the steady and unsteady incompressible viscous flows over a circular cylinder for validation and performance evaluation purposes. It is found that the multigrid method with three levels of grids results in a 75% reduction in CPU time for the steady flow calculation and 55% reduction for the unsteady flow calculation, compared with its single grid counterparts. The results obtained are compared with numerical solutions obtained by other researchers as well as experimental measurements wherever available and good agreements are obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

Multigrid pressure correction techniques for the computation of quasi-incompressible internal flows

A study is reported on the possibility of improving the speed of convergence of existing numerical programmes for the simulation of flow in combustion chambers by applying the multigrid method to the pressure correction phase only. A version of the multigrid algorithm is introduced for this purpose which achieves a 1:10 residual reduction in a single V(1, 1) cycle. The overall decrease in computation time with respect to an industry-standard SIMPLE algorithm with single-grid pressure correction ranges from four to five times for SIMPLE itself and several other well-known algorithms to six times for a newly developed pressure correction strategy we call difference operator triangularization (DOT).     

A PARALLEL BLOCK-STRUCTURED MULTIGRID METHOD FOR THE PREDICTION OF INCOMPRESSIBLE FLOWS

In this paper a parallel multigrid finite volume solver for the prediction of steady and unsteady flows in complex geometries is presented. For the handling of the complexity of the geometry and for the parallelization a unified approach connected with the concept of block-structured grids is employed. The parallel implementation is based on grid partitioning with automatic load balancing and follows the message-passing concept, ensuring a high degree of portability. A high numerical efficiency is obtained by a non-linear multigrid method with a pressure correction scheme as smoother. By a number of numerical experiments on various parallel computers the method is investigated with respect to its numerical and parallel efficiency. The results illustrate that the high performance of the underlying sequential multigrid algorithm can largely be retained in the parallel implementation and that the proposed method is well suited for solving complex flow problems on parallel computers with high efficiency.     

A multigrid semi-implicit finite difference method for the two-dimensional shallow water equations

A multigrid semi-implicit finite difference method is presented to solve the two-dimensional shallow water equations which describe the behaviour of basin water under the influence of the Coriolis force, atmospheric pressure gradients and tides. The semi-implicit finite difference method discretizes implicitly both the gradient of the water elevation in the momentum equations and the velocity divergence in the continuity equations and explicitly the convective terms using an Eulerian–Lagrangian approach. At each time step we apply the multigrid computation to solve the resulting linear, symmetric, pentadiagonal system of discrete equations. The multigrid algorithm, defined on staggered grids, provides accelerated convergence histories. We numerically simulate the water circulation in a closed rectangular basin, centrally crossed by a deeper channel. Moreover, simulation of the circulation in San Pablo Bay shows the high flexibility and applicability of this method to concrete problems. Visualizations of the computed variables, water depth and velocity, are shown by figures. Displays of convergence histories show promising multigrid acceleration. © 1997 John Wiley & Sons, Ltd.     

A coupled multigrid-domain-splitting technique for simulating incompressible flows in geometrically complex domains

This paper describes a domain decomposition numerical procedure for solving the Navier-Stokes equations in regions with complex geometries. The numerical method includes a modified version of QUICK (quadratic upstream interpolation convective kinematics) for the formulation of convective terms and a central difference scheme for the diffusion terms. A second-order-accurate predictor-corrector scheme is employed for the explicit time stepping. Although the momentum equations are solved independently on each subdomain, the pressure field is computed simultaneously on the entire flow field. A multigrid technique coupled with a Schwarz-like iteration method is devised to solve the pressure equation over the composite domains. The success of this strategy depends crucially on appropriate methods for specifying intergrid pressure boundary conditions on subdomains. A proper method for exchanging information among subdomains during the Schwarz sweep is equally important to the success of the multigrid solution for the overall pressure field. These methods are described and subsequently applied to two forced convection flow problems involving complex geometries to demonstrate the power and versatility of the technique. The resulting pressure and velocity fields exhibit excellent global consistency. The ability to simulate complex flow fields with this method provides a powerful tool for analysis and prediction of mixing and transport phenomenon.     

Comparison of pressure correction smoothers for multigrid solution of incompressible flow

We compare the performance of different pressure correction algorithms used as basic solvers in a multigrid method for the solution of the incompressible Navier–Stokes equations on non-staggered grids. Numerical tests were performed on several cases of lid-driven cavity flow using four different pressure correction schemes, including the traditional SIMPLE and SIMPLEC methods as well as novel variants, and varying combinations of underrelaxation parameters. The results show that three of the four algorithms tested are robust smoothers for the multigrid solver and that one of the new methods converges fastest in most of the tests. © 1997 John Wiley & Sons, Ltd.     

点、线接触真实粗糙表面的弹流润滑研究

本文给出了点、线接触的真实粗糙表面的微弹流数值解。在给定随机粗糙表面样本后,求解大小不同的载荷和粗糙的弹流问题。从计算结果可以看出,由于Reynolds方程中速度项的作用,在表面对应粗糙的位置处引起了压力变化,从而因其产生的弹性变形使粗糙变得平滑。对此光滑表面解可以看出,因粗糙引起的压力和膜厚的变化在光滑解附近波动。载荷较大时,压力分节接近固体接触情况。     

The multigrid method for reservoir simulation

This paper describes a way of solving the reservoir simulation pressure equation using multigrid technique. The subroutine MG of four-grid method is presented. The result for 2-D two-phase problem is exactly the same as that of the SOR method and the CPU time is much less than that of the latter one.