三维各向异性叉树网格流场自适应算法研究

建立了三维叉树形网格的数据结构,并将结构网格的有限体积法引入到叉树网格中,建立了相应的NS方程求解方法。在此基础上完善了包括各向异性自适应判别、合并/分裂、网格优化等步骤的算法,并提出了对流场结构进行“保护”性加密的优化加密方式。基于自适应叉树网格对高超声速横向喷流流场进行了数值模拟,捕捉到细致的流场结构,并将壁面压力系数计算值与文献试验值比较,得到了很好的模拟效果,具有较高的流场分辨精度。     

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．     

采用自适应直角网格计算三维增升装置绕流

针对三维增升装置绕流，对存在剪刀叉的不连续外形，基于自适应直角网格，提出并介绍了分区和面搭接技术，采用变长宽比网格，进行了直角网格生成和流场Euler方程数值计算. 根据几何外形的特点，在直角网格生成过程中，以外形不连续面作为分区边界，对初始``根'网格实施分区处理，降低了整个网格的生成难度. 通过基于外形的自适应网格加密，详细描述了剪刀叉外形和缝道，提高了网格质量. 在分区边界面上，基于面搭接技术，构造重叠面积切割算法，实现边界两侧网格间的流场信息传递，保证流场计算中的通量守恒. 采用中心有限体积方法，结合双时间推进算法，完成了两段机翼、带增升襟翼翼身组合体绕流流场的Euler方程数值模拟，对计算结果与实验数据进行了对比，验证了所提方法、算法的合理性和实用性.     

线化欧拉方程的高阶间断有限元数值解法研究

采用高阶间断有限元法于非结构网格上针对复杂外形数值求解声学控制方程------线化欧拉方程. 背景流场采用有限体积法于结构网格求得, 一种高精度数据传递方法将基于有限体积法的背景流场数据传递到声场计算所采用的较为稀疏的非结构网格上, 保证了背景流场信息的完整和精确. 为提高计算效率, 采用了一种更为直接的Quadrature-FreeImplementation技术以及网格分区并行技术. 数值结果表明采用高阶的情况下即使在稀疏的网格上也可以捕捉到细微的声场结构.      

近床面水平圆柱局部冲刷二维数值模拟

为研究近床面水平圆柱的局部冲刷问题,基于N-S方程和有限体积法,在FLUENT中通过二次开发建立了局部冲刷二维数值模型。模型采用标准κ-ε紊流模型来计算水平圆柱周围的流场,同时借助FLUENT软件中的自定义函数功能提取床面剪应力参数来计算该时刻的推移质输沙率及床面节点位移变化值,然后运用动网格技术来模拟床面地形的变化,通过物理模型试验来进行模型验证。结果表明,计算结果与试验结果基本一致,从而证实了冲刷模型的准确性。     

适用于任意网格拓扑和质量的格心有限体积法

针对格心有限体积法的离散精度易受网格类型影响的问题,基于最小二乘原理,提出了一种适用于任意网格拓扑和网格质量的有限体积方法.在解的光滑区能保证二阶精度,可光滑、陡峭地捕捉激波等强间断面.精度与网格无关,且算法统一的特性使其非常适用于网格自适应和多重网格等计算应用,同时也降低了网格生成和流场求解的复杂性.跨音速算例的网格含有多种网格拓扑,计算结果表明发展的线性重构方法(linearreconstruction method,LRM)适用于不同的网格拓扑,计算得到的激波位置准确、陡峭,未产生数值振荡.运用Ringleb流动考查了该方法对低质量网格的收敛性,与传统方法相比,线性重构方法(LRM)不仅平均误差较小,而且误差随网格尺度的收敛性也更好,其精度接近二阶.三段翼型的黏性绕流计算进一步表明网格质量对其精度的影响较小.     

预处理方法在低速弹箭流场计算中的应用

基于Weiss-Smith预处理矩阵和全局截断预处理参数,采用有限体积方法对雷诺平均Navier-Stokes方程进行离散。对流项离散采用二阶线性重构和AUSM ＋-up格式,时间推进方法采用多重网格下的LU-SGS方法。结合M PI消息传递方法,建立了一套计算低速流动的并行数值方法。计算了低速椭球体的流场和气动力,压力系数和切应力系数计算结果与文献实验结果对比吻合度较好。生成了末敏弹的流场计算网格,对绕末敏弹流场进行了数值模拟。对多重网格下多进程的加速比和并行效率进行了测试,显示了程序良好的并行效率。计算的气动力结果与实验结果吻合。综合结果表明：本文的数值方法能够用于低速弹箭流场和气动力计算,为新型弹箭的设计和定型提供保证。     

全机跨音速大迎角绕流的数值分析

应用有限体积法求解Ｅｕｌｅｒ方程计算了真实飞机外形的跨音速大迎角绕流流场及空气动力特性。本方法能自动捕获大后掠机翼前缘脱体涡，侧缘涡，机身体涡以及它们间的相互干扰。计算的机翼压力分布及全机气动力系数与实验值符合良好。表明了本文所采用的计算网格生成技术及流场计算方法是有效、可行的。     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

非结构重叠网格方法研究及应用

航空、航天和兵器技术等领域的研究中存在大量包含运动边界的流场。非结构重叠网格方法是一种高效的处理动边界问题的新方法。围绕相对运动的每个物体单独生成非结构网格,在网格重叠区域通过搜索和插值完成网格系之间的信息传递,提出了动态八叉树搜索算法,发展了绝对坐标系和相对坐标系相结合的流场求解方式,采用二阶精度Van Leer/Hanel格式和四阶Runge-Kutta法分别进行空间和时间离散,形成了一种新的非结构重叠网格算法。对三维Riemann问题的求解结果与精确解能很好吻合,证明了本文的重叠网格算法具有较好的时空离散精度和插值精度。对7.62mm步枪射击过程进行了数值模拟,描述了弹丸离开膛口后膛口流场的发展过程,与实验结果体现的发展过程较为吻合,验证了本文提出的非结构网格算法体系具有较好的计算性能,是研究含动边界复杂流场的一种有效手段。     

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.     

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.     

Adaptive Runge–Kutta discontinuous Galerkin method for complex geometry problems on Cartesian grid

A Cartesian grid method using immersed boundary technique to simulate the impact of body in fluid has become an important research topic in computational fluid dynamics because of its simplification, automation of grid generation, and accuracy of results. In the frame of Cartesian grid, one often uses finite volume method with second order accuracy or finite difference method. In this paper, an h‐adaptive Runge–Kutta discontinuous Galerkin (RKDG) method on Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is developed. A ghost cell immersed boundary treatment with the modification of normal velocity is presented. The method is validated versus well documented test problems involving both steady and unsteady compressible flows through complex bodies over a wide range of Mach numbers. The numerical results show that the present boundary treatment to some extent reduces the error of entropy and demonstrate the efficiency, robustness, and versatility of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Velocity–pressure coupling in finite difference formulations for the Navier–Stokes equations

A new numerical procedure for solving the two‐dimensional, steady, incompressible, viscous flow equations on a staggered Cartesian grid is presented in this paper. The proposed methodology is finite difference based, but essentially takes advantage of the best features of two well‐established numerical formulations, the finite difference and finite volume methods. Some weaknesses of the finite difference approach are removed by exploiting the strengths of the finite volume method. In particular, the issue of velocity–pressure coupling is dealt with in the proposed finite difference formulation by developing a pressure correction equation using the SIMPLE approach commonly used in finite volume formulations. However, since this is purely a finite difference formulation, numerical approximation of fluxes is not required. Results presented in this paper are based on first‐ and second‐order upwind schemes for the convective terms. This new formulation is validated against experimental and other numerical data for well‐known benchmark problems, namely developing laminar flow in a straight duct, flow over a backward‐facing step, and lid‐driven cavity flow. Copyright © 2010 John Wiley & Sons, Ltd.     

Automatic grid generation of complex geometries in Cartesian co-ordinates

A method of automatic grid generation for complex boundaries in Cartesian co-ordinates is proposed in this paper. In addition to the Cartesian grid lines the diagonal segments are used for the approximations of complex geometries in Cartesian co-ordinates. A structured Cartesian grid is employed for the sake of the numerical simplicity and the potential of automatic grid generation. The automatic grid generation is achieved by this diagonal Cartesian method and the accuracy estimations of geometry approximations are given. The approximations of a few complex geometries, such as the multibody system in porous media, lake banks, grooved channels and spheres are shown and analyzed. The proposed method is verified by the numerical solutions of a rotated cavity flow. It is shown that the diagonal Cartesian method improves both the accuracy of geometry approximations and the numerical solution of a rotated cavity flow, comparing with the traditional saw-tooth method in which only Cartesian grid lines are utilized for geometry approximations. The stability and convergence of the proposed method is demonstrated. Finally, the application of the diagonal Cartesian method for the prediction of a grooved channel flow is presented. © 1998 John Wiley & Sons, Ltd.     

Euler analysis of transonic stator-rotor interaction using a finite volume method

A generalized finite volume method that can solve the Euler equations for the stator and rotor parts of stage flow in similar formulations is presented. The method consists of a new moving grid finite volume formulation applied to the rotor region and the existing fixed grid finite volume method used in the stator region, with the data transfer made by an interpolation procedure at the sliding surface in between. The accuracy of the method has been demonstrated on a simple cascade flow before the time-dependent compressor stage flow is fully investigated. The transonic stator-rotor flow interaction is elucidated within the inviscid and rotational flow limit.     

Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming

We present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible fluid flows. The temporal and spatial discretizations of the Navier–Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge–Kutta scheme and compact finite differences, respectively. Using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the Poisson equation to ensure the incompressibility constraint down to machine zero over an optimal grid. For introducing a deformable body in fluid flow, the volume penalization method is used. A Lagrangian structured grid with prescribed motion covers the deformable body which is interacting with the surrounding fluid due to the hydrodynamic forces and the torque calculated on the Eulerian reference grid. An efficient law for controlling the curvature of an anguilliform fish, swimming toward a prescribed goal, is proposed which is based on the geometrically exact theory of nonlinear beams and quaternions. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming and also for a variety of fluid/solid interaction problems.     

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。