复杂无粘流场数值模拟的矩形/三角形混合网格技术

建立了一套模拟复杂无粘流场的矩形／三角形混合网格技术，其中三角形仅限于物面附近，发挥非结构网格的几何灵活性，以少量的网格模拟复杂外型；同时在以外的区域采用矩形结构网格，发挥矩形网格计算简单快速的优势，有效地克服全非结构网格计算方法需要较大内存量和较长ＣＰＵ时间的不足．混合网格系统由修正的四分树方法生成．将ＮＮＤ有限差分与ＮＮＤ有限体积格式有机地融合于混合网格计算，消除了全矩形网格模拟曲边界的台阶效应，同时保证了网格间的通量守恒．数值实验表明本方法在模拟复杂无粘流场方面的灵活性和高效性．     

动态混合网格生成及隐式非定常计算方法

建立了一种基于动态混合网格的非定常数值计算方法. 混合网格由贴体的四边形网格、外场 的多层次矩形网格和中间的三角形网格构成. 当物体运动时，贴体四边形网格随物体运动而 运动，而外场的矩形网格保持静止，中间的三角形网格随之变形；当物体运动位移较大，导 致三角形网格的质量降低，甚至导致网格相交时，在局部重新生成网格. 新网格上的物理量 由旧网格上的物理量插值而得. 为了提高计算效率，采用了双时间步和子迭代相结合的隐式 有限体积格式计算非定常Navier-Stokes方程. 子迭代采用高效的块LU-SGS方法. 利用该 方法数值模拟了NACA0012振荡翼型的无黏和黏性绕流，得到了与实验和他人计算相当一致 的结果.     

An unstructured/structured multi‐layer hybrid grid method and its application

A multi‐layer hybrid grid method is constructed to simulate complex flow field around 2‐D and 3‐D configuration. The method combines Cartesian grids with structured grids and triangular meshes to provide great flexibility in discretizing a domain. We generate the body‐fitted structured grids near the wall surface and the Cartesian grids for the far field. In addition, we regard the triangular meshes as an adhesive to link each grid part. Coupled with a tree data structure, the Cartesian grid is generated automatically through a cell‐cutting algorithm. The grid merging methodology is discussed, which can smooth hybrid grids and improve the quality of the grids. A cell‐centred finite volume flow solver has been developed in combination with a dual‐time stepping scheme. The flow solver supports arbitrary control volume cells. Both inviscid and viscous flows are computed by solving the Euler and Navier–Stokes equations. The above methods and algorithms have been validated on some test cases. Computed results are presented and compared with experimental data. Copyright © 2006 John Wiley & Sons, Ltd.     

基于自适应直角网格的二维全速势方程有限体积解法A finite volume method for 2D Full-Potential equation on adaptive Cartesian grids

为满足亚声速和跨声速飞机概念设计中快速气动计算的需求,研究和发展一种基于自适应直角网格的非线性全速势方程有限体积解法。要点如下。（1）在几何自适应直角网格的基础上,使用结合单元融合的网格切割算法处理物面边界,提出一种修正非贴体切割网格的方法。（2）采用隐式格式结合GM RES算法求解该非线性位流方程,针对流场的自适应来捕捉激波。（3）采用镜像法处理物面边界处的无穿透条件,并提出解析的方法来修正镜像单元的值。（4）针对直角网格的特点,提出在库塔线上插入库塔单元的方法施加库塔条件。NACA0012翼型绕流的算例结果表明,该方法用于亚声速和跨声速气动计算能得到令人满意的结果,且自动化程度高、收敛速度快。     

Large-eddy simulation of flow separation on an airfoil at a high angle of attack and Re = 105 using Cartesian grids

Incompressible flow separating from the upper surface of an airfoil at an 18° angle of attack and a Reynolds number of Re = 10⁵, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data.     

动网格生成技术及非定常计算方法进展综述

对应用于飞行器非定常运动的数值计算方法(包括动态网格技术和相应的数值离散格式)进行了综述.根据网格拓扑结构的不同,重点论述了基于结构网格的非定常计算方法和基于非结构/混合网格的非定常计算方法,比较了各种方法的优缺点.在基于结构网格的非定常计算方法中,重点介绍了刚性运动网格技术、超限插值动态网格技术、重叠动网格技术、滑移动网格技术等动态结构网格生成方法,同时介绍了惯性系和非惯性系下的控制方程,讨论了非定常时间离散方法、动网格计算的几何守恒律等问题.在基于非结构/混合网格的非定常计算方法中,重点介绍了重叠非结构动网格技术、重构非结构动网格技术、变形非结构动网格技术以及变形/重构耦合动态混合网格技术等方法,以及相应的计算格式,包括非定常时间离散、几何守恒律计算方法、可压缩和不可压缩非定常流动的计算方法、各种加速收敛技术等.在介绍国内外进展的同时,介绍了作者在动态混合网格生成技术和相应的非定常方法方面的研究与应用工作.     

一种分子运动和碰撞双重网格DSMC方法研究

基于非结构网格与直角网格相结合的策略,提出一种分子运动和碰撞双重网格DSMC实现方法。通过分子的位置坐标信息,实现运动网格与碰撞网格信息交互,从而结合非结构网格的贴体性和直角网格易于控制子网格数量的优点,同时提出并实现了基于MCS自适应的动态子网格技术以有效限制分子平均碰撞距离,提高了DSMC方法的通用性和计算精度。通过对超声速圆柱绕流和扩张管道的数值模拟,验证该方法的有效性和高精度性。数值结果表明,本文提出的基于分子运动和碰撞双重网格的DSMC方法提高了流场的分辨率,且通过基于MCS自适应的动态子网格技术,有效地降低了流场的平均碰撞距离,提高了碰撞质量和计算精度。     

用鲁棒Riemann求解器和运动重叠网格计算旋翼粘性绕流

发展了一种基于鲁棒Riemann求解器和运动重叠网格技术计算直升机悬停旋翼流场的方法。基于惯性坐标系,悬停旋翼流场是非定常流场,控制方程为可压缩Reynolds平均Navier-Stoke方程,其对流项采用Roe近似Reimann求解器离散,使用改进的五阶加权基本无振荡格式进行高阶重构,非定常时间推进采用含牛顿型LUSGS子迭代的全隐式双时间步方法。为实施旋转运动和便于捕捉尾迹,计算采用运动重叠网格技术。计算得到的桨叶表面压力分布及桨尖涡涡核位置都与实验结果吻合较好。数值结果表明:所发展方法对桨尖涡具有较高的分辨率,对激波具有较好的捕捉能力,该方法可进一步推广到前飞旋翼粘性绕流的计算。     

CartGen: Robust,efficient and easy to implement uniform/octree/embedded boundary Cartesian grid generator

An efficient and easy to implement method to generate Cartesian grids is presented. The presented method generates various kinds of Cartesian grids such as uniform, octree and embedded boundary grids. It supports the variation of grid size along each spatial direction as well as anisotropic and non‐graded refinements. The efficiency and ease of implementation are the main benefits of the presented method in contrast to the alternative methods. Regarding octree grid generation, applying a simple and efficient data compression method permits to store all grid levels without considerable memory overhead. The presented method generates octree grids up to a 13‐level refinement (8192³ grids on the finest level) from a complicated geometry in a few minutes on the traditional desktop computers. The FORTRAN 90 implementation of the presented method is freely available under the terms of the GNU general public license. Copyright © 2007 John Wiley & Sons, Ltd.     

A fast nested multi‐grid viscous flow solver for adaptive Cartesian/Quad grids

A nested multi‐grid solution algorithm has been developed for an adaptive Cartesian/Quad grid viscous flow solver. Body‐fitted adaptive Quad (quadrilateral) grids are generated around solid bodies through ‘surface extrusion’. The Quad grids are then overlapped with an adaptive Cartesian grid. Quadtree data structures are employed to record both the Quad and Cartesian grids. The Cartesian grid is generated through recursive sub‐division of a single root, whereas the Quad grids start from multiple roots—a forest of Quadtrees, representing the coarsest possible Quad grids. Cell‐cutting is performed at the Cartesian/Quad grid interface to merge the Cartesian and Quad grids into a single unstructured grid with arbitrary cell topologies (i.e., arbitrary polygons). Because of the hierarchical nature of the data structure, many levels of coarse grids have already been built in. The coarsening of the unstructured grid is based on the Quadtree data structure through reverse tree traversal. Issues arising from grid coarsening are discussed and solutions are developed. The flow solver is based on a cell‐centered finite volume discretization, Roe's flux splitting, a least‐squares linear reconstruction, and a differentiable limiter developed by Venkatakrishnan in a modified form. A local time stepping scheme is used to handle very small cut cells produced in cell‐cutting. Several cycling strategies, such as the saw‐tooth, W‐ and V‐cycles, have been studies. The V‐cycle has been found to be the most efficient. In general, the multi‐grid solution algorithm has been shown to greatly speed up convergence to steady state—by one to two orders. Copyright © 2000 John Wiley & Sons, Ltd.     

A hybrid building‐block and gridless method for compressible flows

A hybrid building‐block Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian mesh based on a building‐block grid is used as a baseline mesh to cover the computational domain, while the boundary surfaces are represented using a set of gridless points. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time‐accurate solution of the compressible Euler equations. An overall speed‐up factor from six to more than one order of magnitude and a saving in storage requirements up to one order of magnitude for all test cases in comparison with the unstructured grid method are demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

Application of hybrid Cartesian grid and gridless approach to moving boundary flow problems

The paper presents a hybrid Cartesian grid and gridless approach to solve unsteady moving boundary flow problems. Unlike the Chimera clouds of points approach, the hybrid approach uses a Cartesian grid to cover most of the computational domain and a gridless method to calculate a relatively small region adjacent to the body surface, making use of the flexibility of the gridless method in handling surface grid with complicated geometry and the computational efficiency of the Cartesian grid. Four cases were conducted to examine the applicability, accuracy and robustness of the hybrid approach. Steady flows over a single NACA0012 airfoil and dual NACA0012 airfoils at different Mach numbers and angles of attack were simulated. Moreover, by implementing a dynamic hole cutting, node identification and information communication between the Cartesian grid and the gridless regions, unsteady flows over a pitching NACA0012 airfoil (small displacement) and two‐dimensional airfoil/store separation (large displacement) were performed. The computational results were found to agree well with earlier experimental data as well as computational results. Shock waves were accurately captured. The computational results show that the hybrid approach is of potential to solve the moving boundary flow problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical simulation of flow fields induced by a supersonic projectile moving in tubes

Numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed in this paper. Based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions. Both the level set technique and ghost fluid method are used for capturing the moving interface of the projectile implicitly. The numerical results show that complex shock phenomena exist in the transient shock flow, resulting from shock-wave reflection, shock-wave focusing, shock-wave/projectile interaction and shock-wave/contact surface interactions. The relationships between the acceleration of the projectile and the transient shock flow are also discussed in detail.     

Adaptive methods of lines for one-dimensional reaction-diffusion equations

Adaptive and non-adaptive finite difference methods are used to study one-dimensional reaction-diffusion equations whose solutions are characterized by the presence of steep, fast-moving flame fronts. Three non-adaptive techniques based on the methods of lines are described. The first technique uses a finite volume method and yields a system of non-linear, first-order, ordinary differential equations in time. The second technique uses time linearization, discretizes the time derivatives and yields a linear, second-order, ordinary differential equation in space, which is solved by means of three-point, fourth-order accurate, compact differences. The third technique takes advantage of the disparity in the time scales of the reaction and diffusion processes, splits the reaction--diffusion operator into a sequence of reaction and diffusion operators and solves the diffusion operator by means of either a finite volume method or a three-point, fourth-order accurate compact difference expression. The non-adaptive methods of lines presented in this paper may use equaliy or non-equally spaced fixed grids and require a large number of grid points to solve accurately one-dimensional problems characterized by the presence of steep, fast-moving fronts. Three adaptive methods for the solution of reaction-diffusion equations are considered. The first adaptive technique is static and uses a subequidistribution principle to determine the grid points, avoid mesh tangling and node overtaking and obtain smooth grids. The second adaptive technique is dynamic, uses an equidistribution principle with spatial and temporal smoothing and yields a system of first-order, non-linear, ordinary differential equations for the grid point motion. The third adaptive technique is hybrid, combines some features of static and dynamic methods, and uses a predictor-corrector strategy to predict the grid and solve for the dependent variables, respectively. The three adaptive techniques presented in this paper use physical co-ordinates and may employ finite volume or three-point, compact methods. The adaptive and non-adaptive finite difference methods presented in the paper are used to study a decomposition chemical reaction characterized by a scalar, one-dimensional reaction-diffusion equation, the propagation of a one-dimensional, confined, laminar flame in Cartesian co-ordinates and the Dwyer-Sanders model of one-dimensional flame propagation. It is shown that the adaptive moving method presented in this paper requires a smaller number of grid points than adaptive static, adaptive hybrid and non-adaptive methods. The adaptive hybrid method requires a smaller time step than adaptive static techniques, due to the lag between the grid prediction and the solution of the dependent variables. Non-adaptive methods of lines may yield temperature oscillations in front of and behind the flame front if Crank-Nicolson techniques are used to evaluate the time derivatives. Fourth-order accurate methods of lines in space yield larger temperature oscillations than second-order accurate methods of lines, and the magnitude of these oscillations decreases as the time step is decreased. It is also shown that three-point, fourth-order accurate discretizations of the spatial derivatives require the same number of grid points as second-order accurate, finite volume methods, in order to resolve accurately the structure of steep, fast-moving flame fronts.     

基于贴体网格的VOF方法数模流场研究

提出了一种基于VOF方法的模拟具有复杂边界形状结构物附近流场的新算法,BFC—SIMPLE—VOF算法。采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散。提出了基于交错网格的修正SIMPLE算法来迭代求解压力一速度场,修正了贴体坐标下的界面跟踪方法（VOF方法）...     

Calculation of laminar recirculating flows using a local non-staggered grid refinement system

A grid-embedding technique for the solution of two-dimensional incompressible flows governed by the Navier-Stokes equations is presented. A finite volume method with collocated primitive variables is employed to ensure conservation at the interfaces of embedding grids as well as global conservation. The discretized equations are solved simultaneously for the whole domain, providing a strong coupling between regions of different refinement. The formulation presented herein is applicable to uniform or non-uniform Cartesian meshes. The method was applied to the solution of two scalar transport equations, to cavity flows driven by body and shear forces and to a sudden plane contraction flow. The numerical predictions are compared with the exact solutions when available and with experimental data. The results show that neither the convergence rate nor the stability of the method is affected by the presence of embedded grids. Embedded grids provide a better distribution of grid nodes over the computational domain and consequently the solution accuracy was improved. The grid-embedding technique proved also that significant savings in computing time could be achieved.     

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

An Adaptive Grid Eulerian Method for the Computation of Free Surface Flows

A numerical scheme for the prediction of free surface flows is presented and investigated. The method is based on an adaptive grid Eulerian finite-volume method, where non-orthogonal boundary-fitted moving grids are employed to follow the free surface. The underlying flow solver consists in a pressure-correction scheme of SIMPLE type with multigrid acceleration, which is iteratively combined with the moving grid technique. Several numerical examples are considered to illustrate the capabilities of the approach.     

A technique of flux reconstruction at the interfaces of nonconforming grids for aeroacoustic simulations

A flux reconstruction technique is presented to perform aeroacoustic computations using implicit high-order spatial schemes on multiblock structured grids with nonconforming interfaces. The use of such grids, with mesh spacing discontinuities across the block interfaces, eases local mesh refinements, simplifies the mesh generation process, and thus facilitates the computation of turbulent flows. In this work, the spatial discretization consists of sixth-order finite-volume implicit schemes with low-dispersion and low-dissipation properties. The flux reconstruction is based on the combination of noncentered schemes with local interpolations to define ghost cells and compute flux values at the grid interfaces. The flow variables in the ghost cells are calculated from the flow field in the grid cells using a meshless interpolation with radial basis functions. In this study, the flux reconstruction is applied to both plane and curved nonconforming interfaces. The performance of the method is first evaluated by performing two-dimensional simulations of the propagation of an acoustic pulse and of the convection of a vortex on Cartesian and wavy grids. No significant spurious noise is produced at the grid interfaces. The applicability of the flux reconstruction to a three-dimensional computation is then demonstrated by simulating a jet at a Mach number of 0.9 and a diameter-based Reynolds number of 4×10⁵ on a Cartesian grid. The nonconforming grid interface located downstream of the jet potential core does not appreciably affect the flow development and the jet sound field, while reducing the number of mesh points by a factor of approximately two.