基于复合叉树的自适应笛卡尔网格应用研究

采用复合叉树自适应笛卡尔网格和有限体积法求解三维Euler方程,在网格生成过程中,以模型几何外形、模型表面曲率为基础,构建了基于复合叉树的网格生成和加密方法。在流场计算过程中,又针对流场变化特征,建立了基于复合叉树的网格各向异性拆分模式,同时采用以中心差分为基础的Jameson有限体积法。通过对M6机翼在跨音速情况下的数值仿真,表明计算结果与风洞实验结果符合良好,同时也表明本算法具有高分辨率、节省机时,提高计算效率等特点。     

网格自适应技术在复杂外形流场模拟中的应用

建立了一套适用于非结构混合网格自适应方法,针对激波和涡的不同特征采用不同加密探测器,各向异性加密棱柱单元并沿物面法向方向剖分所有棱柱层,各向异性剖分四面体单元,并保证四面体与棱柱交界面上网格协调。构造Hermit插值近似投影物面新加网格点和基于Laplacian光滑方法对空间网格进行优化。通过网格自适应加密,使用Roe格式计算高超声速球头绕流的红玉现象得到明显减轻。F16飞机含激波和脱体涡的流场自适应计算表明,网格加密集中在激波面和涡核附近区域,激波和涡计算更准确。     

简单高效的面向对象四叉树有限元网格生成技术研究

用面向对象的思想和方法与四叉树有限元网格生成结合 ,创建或改进了网格生成各个阶段的算法和实现方式 ,并在面向对象语言 VC 6 .0中得以实现。能快速、高效地生成适用于任何复杂边界的四叉树有限元网格 ,易于自适应 ,易于局部加密和稀疏化。     

基于建筑风场数值模拟的网格层块加密法

在建筑风场的数值模拟中,当前普遍采用的离散网格多是计算前一次性布置的固定网格,通常很难适应实际流场变量的变化要求.为提高数值模拟的精度,基于结构化同位网格系统及控制容积离散微分方程的方法,将适应性网格局部加密(AMR)的思想引入到采用压力校正迭代算法的建筑风场模拟中,提出了一种半自适应的层块网格加密方法.该方法可结合误差分析对误差较大的区域网格实行自动判别并实施逐层块状加密.算例分析表明,该方法能在较高的效益下提高数值解的精度.     

基于叉树法的自适应有限元局部网格加密研究

本文以叉树法网格生成技术为基础，提出了效率高，易实现的局部网格加密步骤，同时设计了相互匹配的网格数据结构和树数据结构以及局部网格修正算法用以支持本文所提出的局部网格加密步骤，最后，给出了局部网格加密例子，用以证明本文所提出的方法可以很容易地生成任意密度分布的网格，对于实施自适应ｈ－方案是十分有利的。     

结合自适应网格的基于特征线方程的分离算法

提出一种新的网格自适应方法:在需要加密的网格单元中心加入新结点,并对加密后的相邻三角形网格单元进行公共边变换, 构成新的网格单元. 与传统的在网格边界中点加入新节点的自适应方法相比,新方法可以更加灵活地控制网格密度,加密后的网格继承原先的网格质量不发生畸变,并且算法编程简便,容易实现. 将自适应网格生成方法和基于特征线方程的分离算法相结合,对空腔内不可压缩黏性流动进行了计算. 在特征线方向上进行时间步离散,动量方程求解过程中采用非增量型分离算法. 计算中,把求解变量梯度值作为判定准则,在变化剧烈的区域进行网格局部加密. 计算结果表明该组合算法有很好的计算精度,并有效减少了计算时间和存储量.      

福建海岸带地质环境背景与海水入侵的形成条件探讨

提出一种新的网格自适应方法：在需要加密的网格单元中心加入新结点,并对加密后的相邻 三角形网格单元进行公共边变换, 构成新的网格单元. 与传统的在网格边界中点加入新节点的自 适应方法相比,新方法可以更加灵活地控制网格密度,加密后的网格继承原先的网格质量不 发生畸变,并且算法编程简便,容易实现. 将自适应网格生成方法和基于特征线方程的分离 算法相结合,对空腔内不可压缩黏性流动进行了计算. 在特征线方向上进行时间步离散,动 量方程求解过程中采用非增量型分离算法. 计算中,把求解变量梯度值作为判定准则,在 变化剧烈的区域进行网格局部加密. 计算结果表明该组合算法有很好的计算精度,并有效减 少了计算时间和存储量.     

二维自适应非结构网格DSMC并行算法研究

研究了二维自适应非结构网格DSMC并行算法实现的过程.首先提出了一类非结构网格自适应策略,有效降低了网格尺度对计算结果的影响,提高了流场的分辨率;然后基于PC-CLUSTER群机并行体系结构与消息传递库MPI并行环境,利用分区并行思想,设计了非结构网格DSMC并行算法,节约了计算时间.利用For-tran90的动态分配内存技术编制了通用计算程序;最后对过渡流域高超声绕流进行了数值模拟,计算结果初步验证了算法的可行性与有效性.     

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.     

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。     

The use of dynamic grid adaptation algorithms for the modelling of flow around a circular cylinder in sub‐critical flow regime

In the present study a dynamic grid adaptation (DGA) algorithm is utilized for predicting flow around a circular cylinder in sub‐critical flow regime at a Reynolds number of 1.4×10⁵. The reason for adopting a DGA algorithm is the unsteadiness of the flow field which makes a conventional mesh inefficient. The concept being adopted is to concentrate mesh refinement in regions with high gradients and high turbulent viscosity, while in the region further downstream where the flow is fully developed a coarser mesh will develop and turbulence is modelled with the large eddy simulation (LES) turbulence model. The aim of the study is to present an appropriate variable for mesh refinement, which accomplishes a high rate of mesh refinement in the region with high gradients. The new variable is a product of the local mesh cell size and the rate of strain and includes two additional variables to allow control over the refinement behaviour. The results are compared with experimental data at the corresponding Reynolds number and also with numerical results obtained with conventional mesh. It is demonstrated that DGA algorithms can give results of a very high quality for a mesh that is significantly smaller than for a conventional mesh. Copyright © 2003 John Wiley & Sons, Ltd.     

Robust control volume finite element methods for numerical wave tanks using extreme adaptive anisotropic meshes

Multiphase inertia-dominated flow simulations, and free surface flow models in particular, continue to this day to present many challenges in terms of accuracy and computational cost to industry and research communities. Numerical wave tanks and their use for studying wave-structure interactions are a good example. Finite element method (FEM) with anisotropic meshes combined with dynamic mesh algorithms has already shown the potential to significantly reduce the number of elements and simulation time with no accuracy loss. However, mesh anisotropy can lead to mesh quality-related instabilities. This article presents a very robust FEM approach based on a control volume discretization of the pressure field for inertia dominated flows, which can overcome the typically encountered mesh quality limitations associated with extremely anisotropic elements. Highly compressive methods for the water-air interface are used here. The combination of these methods is validated with multiphase free surface flow benchmark cases, showing very good agreement with experiments even for extremely anisotropic meshes, reducing by up to two orders of magnitude the required number of elements to obtain accurate solutions.     

Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh

We developed a framework for a distributed-memory parallel computer that enables dynamic data management for adaptive mesh refinement and load balancing. We employed simple data structure of the building cube method (BCM) where a computational domain is divided into multi-level cubic domains and each cube has the same number of grid points inside, realising a multi-level block-structured Cartesian mesh. Solution adaptive mesh refinement, which works efficiently with the help of the dynamic load balancing, was implemented by dividing cubes based on mesh refinement criteria. The framework was investigated with the Laplace equation in terms of adaptive mesh refinement, load balancing and the parallel efficiency. It was then applied to the incompressible Navier–Stokes equations to simulate a turbulent flow around a sphere. We considered wall-adaptive cube refinement where a non-dimensional wall distance y⁺ near the sphere is used for a criterion of mesh refinement. The result showed the load imbalance due to y⁺ adaptive mesh refinement was corrected by the present approach. To utilise the BCM framework more effectively, we also tested a cube-wise algorithm switching where an explicit and implicit time integration schemes are switched depending on the local Courant-Friedrichs-Lewy (CFL) condition in each cube.     

Anisotropic mesh adaptation: towards user‐independent,mesh‐independent and solver‐independent CFD. Part III. Unstructured meshes

The present paper is the third article in a three‐part series on anisotropic mesh adaptation and its application to two‐ and three‐dimensional, structured and unstructured meshes. This third paper concerns the application of the full adaptation methodology to 2‐D unstructured meshes, including all four mesh modification strategies presented in Part I, i.e. refinement/coarsening, edge swapping and node movement. The mesh adaptation procedure is validated through a careful monitoring of a single adaptation step and of the solution–adaptation loop. Independence from the initial mesh and from the flow solver is illustrated. The efficiency of the overall methodology is investigated on relevant laminar and turbulent flow benchmarks. Copyright © 2002 John Wiley & Sons, Ltd.     

Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

This paper presents an anisotropic adaptive finite element method (FEM) to solve the governing equations of steady magnetohydrodynamic (MHD) duct flow. A residual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu estimates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.     

基于2D网格的轴对称浸没边界法

浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.      

辛解析奇异元在动荷载作用下V型切口问题中的应用

利用辛解析奇异单元,结合时域精细算法,研究了动荷载作用下的含平面V型切口问题。时域上,采用时域精细算法,并结合自适应算法控制展开项数,保证了计算精度。空间域上,切口尖端附近采用辛解析奇异单元,其余区域采用常规有限单元,避免了局部网格加密。本文使用的辛解析奇异单元不需要过渡单元和局部网格加密,且能够通过奇异单元内部的参数关系直接给出切口尖端的应力强度因子,不需要复杂的后处理过程。数值结果表明,本文方法具有良好的精度和稳定性,可以准确地计算动态应力强度因子。     

The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

The implementation of an adaptive mesh‐embedding (h‐refinement) scheme using unstructured grid in two‐dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an‐isotropic refinement in the interfacial cells between refined and non‐refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high‐speed driven cavity flow. The results show an improved flow resolution as compared with that of un‐adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near‐continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non‐uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd.     

An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.