三维非结构聚合多重网格法数值模拟研究

在三维非结构网格上应用聚合式多重网格技术来加速Euler方程的收敛过程．自行设计了一种高效率的网格聚合方法．采用四重三维非结构网格，在每一层网格上采用有限体积法进行计算．通过对M6翼型的数值求解验证了多重网格加速收敛的高效性．     

全机绕流Euler方程多重网格分区计算方法

全机三维复杂形状绕流数值求解只能采用分区求解的方法,本文采用可压缩Euler方程有限体积方法以及多重网格分区方法对流场进行分区计算。数值方法采用改进的van Leer迎风型矢通量分裂格式和MUSCL方法,基于有限体积方法和迎风型矢通量分裂方法,建立一套处理子区域内分界面的耦合条件。各个子区域之间采用显式耦合条件,区域内部采用隐式格式和局部时间步长等,以加快收敛速度。计算结果飞机表面压力分布等气动力特性与实验值进行了比较,二者基本吻合。计算结果表明采用分析“V”型多重网格方法,能提高计算效率,加快收敛速度达到接近一个量级。根据全机数值计算结果和可视化结果讨论了流场背风区域旋涡的形成过程。     

跨音速大迎角绕流的Euler方程数值模拟

采用保角变换与代数方法相结合，生成全场统一的贴体、正交Ｏ－Ｈ型网格．采用有限体积法求解Ｅｕｌｅｒ方程，模拟具有歼击机外形的全机及翼身组合体大迎角跨音速绕流．计算表明，法向力系数、气动中心位置及压力分布的计算结果与实验结果吻合良好     

高超声速舵面颤振的数值模拟影响因素研究

针对某高超声速舵面颤振风洞试验模型开展了数值模拟研究,采用多种气动力模型和耦合迭代策略,研究对颤振预测结果的影响。计算结果表明,采用三阶活塞理论、统一升力面理论、Euler方程和N-S方程的颤振动压预测结果较接近,与试验值误差均在7%以内。采用时域方法计算时,松耦合方法的误差较大,超过15%。同时还发现,支撑机构会带来激波边界层干扰效应,一定程度上提高了颤振动压,考虑该因素的预测结果与试验值更接近。     

非结构网格热化学非平衡辐射流场数值计算

针对三维热化学非平衡辐射流场设计了基于非结构网格的数值计算方法. 根据原子分子光谱理论逐条计算了100$\sim$1\,500\,nm间N, O, N$^{ + }$, O$^{ + }$的谱线以及N计算流体力学; 辐射; 热化学非平衡; 非结构网格; 有限体积法针对三维热化学非平衡辐射流场设计了基于非结构网格的数值计算方法.根据原子分子光谱理论逐条计算了100～1 500nm间N,O,N+,O+的谱线以及N2,O2,NO,N+2等分子的10个谱带,特别分析了NO的β'带,γ'带,δ带和ε带的辐射特性.采用耦合辐射的双温模型计算热化学非平衡流场,辐射源项通过直接求解辐射输运方程RTE(radiative transport equation)获得.在空间和方向上分别离散后,利用有限体积法求解不同方向上的辐射输运方程.计算得出了再入飞行器前驻点的辐射强度分布.采用该数值方法计算了MUSES-C模型在速度为11.6km/s时的绕流流场及前驻点处的辐射热流密度.并通过对比分析了热辐射对流场的影响.     

基于SIMPLER算法的多重网格方法研究

以二维方腔顶盖驱动流为模型,将多重网格方法和SIMPLER算法进行耦合,对不同雷诺数下多重网格加速SIMPLER算法和SIMPLER算法的计算效率进行了对比,数值计算表明:多重网格加速SIMPLER算法不仅能够解决SIMPLER算法不能准确模拟较高雷诺数流场的问题,而且其计算效率远远高于SIMPLER算法.本文也对松弛因子的选取、多重网格实现形式以及网格层数对多重网格加速SIMPLER算法的影响进行了研究,从而为多重网格加速SIMPLER算法的实施提供了计算技术.     

非结构网格上p型多重网格法流场数值模拟

在二维、三维非结构网榕上,针对间断Galerkin方法计算量大、收敛慢的缺点将p型多重网格方法应用于该方法求解跨音速Euler方程,提高计算效率。p型多重网格方法是通过对不同阶次多项式近似解进行递归迭代求解,来达到加速收敛。文中对高阶近似(p＞0)使用显式格式,最低阶近似(p=0)采用隐式格式。NACA0012翼型和O...     

CFD多块网格生成新进展

网格生成是计算流体力学的重要组成部分,多块网格在CFD实践中获得了广泛的应用．结合对网格生成技术规范和网格生成系统的讨论,综述了多块网格近年来的新进展,重点评述了网格拓扑和网格拼接技术（包括所谓的连续拼接、非结构拼接和广义拼接）,完整飞机外形多块网格生成策略,自动分块技术以及相应的块合井技术,CAD和CFD之间的数据交换技术和基于NURBS的曲面网格生成技术,网格质量分析和控制技术,若干网格生成新方法,以及多块网格在航空气动力数值模拟中的应用．      

基于Voronoi cells的二维不规则自适应网格的生成及其应用

基于Voronoi cells的数据结构和算法，给出了一种二维不规则自适应网格的生成方法，用VisualC＋＋语言在微机上开发了Windows环境下网格自动生成的可视化软件。既可以得到Voronoi cells网格，也可得到相应的Delaunay triangles网格，网格生成的实例表明，本文方法所得到的网格非常适合于多尺度系统的流动问题的计算，具有较好的应用前景。     

一种简单快速的多块网格生成方法

利用有限元中的形函数进行网格插值映射分块生成网格,构造了一种块网格拓扑结构,使得块与相邻块之间自动组合,并利用该方法对二维、三维复杂区域进行分块网格生成,说明该方法生成的网格质量较好,适合于复杂区域分块求解。     

An aspect ratio agglomeration multigrid for unstructured grids

A robust aspect ratio‐based agglomeration algorithm to generate high quality of coarse grids for unstructured and hybrid grids is proposed in this paper. The algorithm focuses on multigrid techniques for the numerical solution of Euler and Navier–Stokes equations, which conform to cell‐centered finite volume special discretization scheme, combines vertex‐based isotropic agglomeration and cell‐based directional agglomeration to yield large increases in convergence rates. Aspect ratio is used as fusing weight to capture the degree of cell convexity and give an indication of cell stretching. Agglomeration front queue is established to propagate inward from the boundaries, which stores isotropic vertex and also high‐stretched cell marked with different flag according to aspect ratio. We conduct the present method to solve Euler and Navier–Stokes equations on unstructured and hybrid grids and compare the results with single grid as well as MGridGen, which shows that the present method is efficient in reducing computational time for large‐scale system equations. Copyright © 2013 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.     

A check on the energy method of predicting blade transonic stall flutter

An improved structural dynamic model of an oscillating blade in two degrees of freedom is combined with an unsteady aerodynamic model for the transonic flow about a cascade with separation, which results in a coupled system. The system is solved in an iterative way between the two models. As a check on the current energy methods, the stall flutter boundaries for two real rotors are predicted by using the present method and the results are compared with the experiments and those predicted by using an energy method.     

A semi-coarsening strategy for unstructured multigrid based on agglomeration

Extending multigrid concepts to the calculation of complex compressible flow is usually not straightforward. This is especially true when non-embedded grid hierarchies or volume agglomeration strategies are used to construct a gradation of unstructured grids. In this work, a multigrid method for solving second-order PDE's on stretched unstructured triangulations is studied. The finite volume agglomeration multigrid technique originally developed for solving the Euler equations is used (M.-H. Lallemand and A. Dervieux, in Multigrid Methods, Theory, Applications and Supercomputing, Marcel Dekker, 337–363 (1988)). First, a directional semi-coarsening strategy based on Poisson's equation is proposed. The second-order derivatives are approximated on each level by introducing a correction factor adapted to the semi-coarsening strategy. Then, this method is applied to solve the Poisson equation. It is extended to the 2D Reynolds-averaged Navier–Stokes equations with appropriate boundary treatment for low-Reynolds number turbulent flows. © 1998 John Wiley & Sons, Ltd.     

An efficient parallel algebraic multigrid method for 3D injection moulding simulation based on finite volume method

Elapsed time is always one of the most important performance measures for polymer injection moulding simulation. Solving pressure correction equations is the most time-consuming part in the mould filling simulation using finite volume method with SIMPLE-like algorithms. Algebraic multigrid (AMG) is one of the most promising methods for this type of elliptic equations. It, thus, has better performance by contrast with some common one-level iterative methods, especially for large problems. And it is also suitable for parallel computing. However, AMG is not easy to be applied due to its complex theory and poor generality for the large range of computational fluid dynamics applications. This paper gives a robust and efficient parallel AMG solver, A1-pAMG, for 3D mould filling simulation of injection moulding. Numerical experiments demonstrate that, A1-pAMG has better parallel performance than the classical AMG, and also has algorithmic scalability in the context of 3D unstructured problems.     

Numerical computation of unsteady incompressible flow in complex geometry using a composite multigrid technique

This paper presents a composite multigrid method and its application to a geometrically complex flow. The treatment of the interior boundary conditions within a composite multigrid strategy is described in detail for a 1D model equation. For the Navier-Stokes equations a staggered grid technique is adopted for spatial discretization and a fractional step method is used for the time advance. Lid-driven cavity flows are used to demonstrate the effectiveness of the method.     

A sliding interface method for unsteady unstructured flow simulations

The objective of this work is to develop a sliding interface method for simulations involving relative grid motion that is fast and efficient and involves no grid deformation, remeshing, or hole cutting. The method is implemented into a parallel, node‐centred finite volume, unstructured viscous flow solver. The rotational motion is accomplished by rigidly rotating the subdomain representing the moving component. At the subdomain interface boundary, the faces along the interface are extruded into the adjacent subdomain to create new volume elements forming a one‐cell overlap. These new volume elements are used to compute a flux across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are determined by linear interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. The grid on the interface surface is arbitrary. The boundary between the two subdomains is completely independent from one another; meaning that they do not have to connect in a one‐to‐one manner and no symmetry or pattern restrictions are placed on the grid. A variety of numerical simulations were performed on model problems and large‐scale applications to examine conservation of the interface flux. Overall solution errors were found to be comparable to that for fully connected and fully conservative simulations. Excellent agreement is obtained with theoretical results and results from other solution methodologies. Copyright © 2006 John Wiley & Sons, Ltd.     

A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains

A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non-orthogonal curvilinear co-ordinate system and are discretized on a non-staggered grid. A semi-implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter-grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well-posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder-accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.     

Numerical investigation of supersonic plate flutter using the exact aerodynamic theory

In classical investigations of panel flutter it is usually assumed that the gas pressure acting on the plate can be calculated within the framework of the piston theory, an approximation exact for high Mach numbers. The loss of stability revealed in these investigations is of the “coupled” type, involving the interaction of two oscillation modes. Recently, the use of asymptotic methods revealed another single-mode type of stability loss, which cannot be obtained within the framework of the piston theory. In the present study this type of stability loss is investigated numerically using the Bubnov-Galerkin method.