任意区域上的粒子均匀分布方法

给出了任意区域内粒子的Voronoi面积均匀划分的方法,对给定的区域边界点,先由边界点得到边界粒子,再利用分布函数结合Delaunay加点算法得到内部粒子,这种方法可以得到一般的区域上粒子的均匀分布。这里给出了一个流体力学中利用SPH方法模拟内爆问题的例子,算例表明,均匀分布可以得到更高的无网格方法数值模拟精度。     

基于刚（粘）塑性流动理论的自然单元法研究

将自然单元法与刚（粘）塑性流动理论相结合,对自然单元法在金属塑性成形过程数值模拟中的应用进行了研究。采用基于Voronoi图和Delaunay三角化结构的Non-Sibsonian插值方法构造近似速度场向量,实现无网格方法中速度边界条件的直接精确施加,提出了基于刚（粘）塑性流动理论的无网格自然单元法。运用不完全广义变分...     

基于修正光滑粒子流体动力学算法的低能量耗散数值波浪水池开发

目前, 无网格光滑粒子流体动力学SPH粒子法在波浪与结构物相互作用研究方面得到广泛应用, 但该方法模拟波浪远距离传播时, 常常面临严重的能量耗散问题, 导致波高非物理性降低, 给大范围海域、长时间作用下的波-物耦合作用研究带来一定困难. 对此, 本文采用一种核函数修正算法, 在确保粒子间相互作用对称性的同时, 改进压力梯度离散项的计算精度, 设法解决SPH方法中能量非物理性耗散的难题. 相较于前人减缓能量非物理性衰减的方法, 本文的修正SPH算法避免了自由液面搜索等复杂处理过程, 并能保证动量守恒特性. 数值结果中, 采用振荡液滴、规则波、不规则波等算例, 验证本修正SPH算法的准确性和有效性. 结果表明, 该修正SPH算法能准确模拟振荡液滴形态变化, 且动能保持较好守恒性. 通过数值水池与物理水池两者规则波与不规则波结果的对比分析表明, 基于本文修正SPH算法建立的数值波浪水池具有较好的抗能量衰减效果, 能实现长时间、远距离波浪传播的准确模拟. 此外, 本算法能在低光滑长度系数条件下, 实现精确模拟, 将极大缩减三维SPH模拟的时间, 从而节约计算成本.      

高质量点集的快速局部网格生成算法

高效及高质量的局部网格生成算法是基于节点有限元并行方法设计的关键。泡泡布点算法能够在复杂区域上不经过人工干预生成高质量的节点集,本文提出了基于该方法所生成的节点集的快速局部网格生成算法。该算法充分利用泡泡布点方法提供的节点集及节点邻接链表信息,避免了桶数据结构的建立以及节点的局部搜索过程,只需应用Delaunay三角剖分的外接圆准则从中心节点的邻接链表中去除极少数的非卫星点,可快速地生成局部网格,比现有的局部网格生成算法更为快捷。算例结果表明,该算法高效可靠,生成网格与Delaunay三角剖分网格一致。     

应用基于GPU的SPH方法模拟二维楔形体入水砰击问题

光滑粒子流体动力学(SPH)法是一种无网格的拉格朗日效值方法,广泛应用于计算流体领域模拟复杂自由表面流问题.SPH方法的主要缺点就是计算量过大,而基于GPU的并行计算方法可使SPH计算得到有效加速.本文应用基于GPU的SPH并行计算方法研究了二维楔形体的入水砰击问题.数值计算结果与文献中对应的解析解比较一致,验证了基于GPU的SPH方法的精度和可靠性.仿真结果同时显示基于GPU的并行计算方法可使SPH计算速度得到显著提高.     

基于ALE方法的3D充填流动模拟

基于任意拉格朗日-欧拉方法发展了三维充填流动的数值模拟方案.该方案采用ALE方法准确地追踪移动自由面的位置并避免了网格扭曲;基于移动最小二乘曲面拟合方法提出了移动自由面上网格节点重定位方法,将充填流动的网格更新过程简化为自由面附近的局部网格重划分过程,并通过分级多面体三角剖分实现,减小了网格划分的计算量,实现了实时网格生成.给出的数值算例结果表明了该数值模型对三维充填流动模拟的有效性.     

多相流动的光滑粒子流体动力学方法研究综述

光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)具有粒子方法的无网格和全拉格朗日特征, 适用于具有界面大变形、不连续性和多物理场的多相流的高精度模拟. SPH方法模拟多相流已有大量报道, 具体的实现方式也大不相同. 本文首先阐述了采用SPH方法模拟流体的基本控制方程, 以及求解过程中需要考虑的流体压力求解、表面张力、固体边界等问题. 整理和总结了基于SPH方法进行多相流模拟的主要实现方式: (1)双流体模型的拉格朗日求解器: 两相离散为两组独立SPH粒子, 并用显式相间作用耦合两相; (2)多相SPH方法: SPH方法对多相流模拟的自然延伸, 相间作用由SPH参数隐式描述; (3) SPH与其他离散方法的耦合: 差异较大的两相各自采用不同离散方法, 发挥不同拉格朗日方法的优点; (4) SPH和基于网格方法的耦合: 网格方法处理简单的单相流动主体, 获得精度和效率间的平衡. 另外, 还在模拟参数物理化等方面论述了与SPH方法模拟多相流相关的一些改进和修正方法, 并在最后讨论和建议了提高多相流SPH模拟效率和精度的措施.      

光滑粒子动力学方法的发展与应用

光滑粒子动力学(smoothed particle hydrodynamics,SPH)是一种拉格朗日型无网格粒子方法,已经成功地应用到了工程和科学的众多领域.SPH使用粒子离散及代表所模拟的介质,并且基于粒子体系估算和近似介质运动的控制方程.本文分析和综述了SPH模拟方法的发展历程、数值方法与应用进展.介绍了SPH方法的基本思想;从连续性、边界处理、稳定性和计算效率4个方面阐述了SPH方法的研究现状;介绍了SPH方法近年来在可压缩流动、不可压缩流动以及弹塑性材料高速变形与失效方面的一些典型应用;并对SPH方法的发展与应用进行了预测与展望.      

三维约束Delaunay三角化的边界恢复和薄元消除方法

提出一种有效的三维约束Delaunay三角剖分的边界恢复算法，该算法综合了P．L．George算法和N．P．Weatherill算法的优点，通过将约束边和约束面加以恢复，保持了实体边界的完整性，解决了经典Delaunay算法不能剖分凹域的问题，从而实现了复杂三维实体的网格剖分。提出了一种简易而有效的消除薄元方法——薄元分解法，彻底解决了三维Delaunay三角剖分过程中所产生的薄元问题。实践证明，本文提出的边界恢复算法和薄元消除算法健壮有效，生成网格的质量高，并且易于实现。     

三维溃坝流的光滑粒子动力学方法模拟

采用光滑粒子动力学SPH(Smoothed Particle Hydrodynamics)方法对三维溃坝流问题进行了数值模拟。为了逼真地模拟出坝内水体与壁面间相互作用而产生的水花飞溅、融合以及近壁面流动等现象,加入了混合长度形式的湍流模型。为了有效地防止粒子穿透固壁,提出了一种新型的适合三维数值模拟的固壁边界处理方法。应用SPH方法对三维溃坝流进行了数值模拟,并分别考虑了未添加障碍物和添加圆柱障碍物两种情形。计算结果表明,改进SPH方法能够精细地捕捉溃坝流在不同时刻的自由液面,并获得稳定而精确的数值结果。     

SPH computation of plunging waves using a 2‐D sub‐particle scale (SPS) turbulence model

The paper presents a 2‐D large eddy simulation (LES) modelling approach to investigate the properties of the plunging waves. The numerical model is based on the smoothed particle hydrodynamics (SPH) method. SPH is a mesh‐free Lagrangian particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The Smagorinsky model is used as the turbulence model due to its simplicity and effectiveness. The proposed 2‐D SPH–LES model is applied to a cnoidal wave breaking and plunging over a mild slope. The computations are in good agreement with the documented data. Especially the computed turbulence quantities under the breaking waves agree better with the experiments as compared with the numerical results obtained by using the k–ε model. The sensitivity analyses of the SPH–LES computations indicate that both the turbulence model and the spatial resolution play an important role in the model predictions and the contributions from the sub‐particle scale (SPS) turbulence decrease with the particle size refinement. Copyright © 2006 John Wiley & Sons, Ltd.     

A POD reduced‐order 4D‐Var adaptive mesh ocean modelling approach

Inflow and outflow boundary conditions are essential for the application of computational fluid dynamics to many engineering scenarios. In this paper we present a new boundary condition implementation that enables the simulation of flow through permeable boundaries in the Lagrangian mesh‐free method, smoothed particle hydrodynamics (SPH). Each permeable boundary is associated with an inflow or outflow zone outside the domain, in which particles are created or removed as required. The analytic boundary condition is applied by prescribing the appropriate variables for particles in an inflow or outflow zone, and extrapolating other variables from within the domain. Characteristic‐based non‐reflecting boundary conditions, described in the literature for mesh‐based methods, can be implemented within this framework. Results are presented for simple one‐dimensional flows, quasi‐one‐dimensional compressible nozzle flow, and two‐dimensional flow around a cylinder at Reynolds numbers of 40 and 100 and a Mach number of 0.1. These results establish the capability of SPH to model flows through open domains, opening a broad new class of applications. Copyright © 2008 John Wiley & Sons, Ltd.     

任意平面区域的变尺寸有限元网格划分

利用任意平面域边界表述中的拓年要素定义网格的控制信息,通过引入节点间距函数来控制区域内网格尺寸变化,并将结合前沿生成法和Ｄｅｌａｕｎａｙ三角化方法的优点,优先处理前沿的最长边,尽可能在局部生成边长逐渐减小的Ｄｅｌａｕｎａｙ三角形,最终实验区域内网格的疏密过渡。     

A Voronoi‐based ALE solver for the calculation of incompressible flow on deforming unstructured meshes

An Arbitrary Lagrangian–Eulerian method for the calculation of incompressible Navier–Stokes equations in deforming geometries is described. The mesh node connectivity is defined by a Delaunay triangulation of the nodes, whereas the discretized equations are solved using finite volumes defined by the Voronoi dual of the triangulation. For prescribed boundary motion, an automatic node motion algorithm provides smooth motion of the interior nodes. Changes in the connectivity of the nodes are made through the use of local transformations to maintain the mesh as Delaunay. This allows the nodes and their associated Voronoi finite volumes to migrate through the domain in a free manner, without compromising the quality of the mesh. An MAC finite volume solver is applied on the Voronoi dual using a cell‐centred non‐staggered formulation, with cell‐face velocities being calculated by the Rhie–Chow momentum interpolation. Advective fluxes are approximated with the third‐order QUICK differencing scheme. The solver is demonstrated via its application to a driven cavity flow, and the flow about flapping aerofoil geometries. Copyright © 2010 John Wiley & Sons, Ltd.     

Coupling finite difference method with finite particle method for modeling viscous incompressible flows

A hybrid approach to couple finite difference method (FDM) with finite particle method (FPM) (ie, FDM-FPM) is developed to simulate viscous incompressible flows. FDM is a grid-based method that is convenient for implementing multiple or adaptive resolutions and is computationally efficient. FPM is an improved smoothed particle hydrodynamics (SPH), which is widely used in modeling fluid flows with free surfaces and complex boundaries. The proposed FDM-FPM leverages their advantages and is appealing in modeling viscous incompressible flows to balance accuracy and efficiency. In order to exchange the interface information between FDM and FPM for achieving consistency, stability, and convergence, a transition region is created in the particle region to maintain the stability of the interface between two methods. The mass flux algorithm is defined to control the particle creation and deletion. The mass is updated by N-S equations instead of the interpolation. In order to allow information exchange, an overlapping zone is defined near the interface. The information of overlapping zone is obtained by an FPM-type interpolation. Taylor-Green vortices and lid-driven shear cavity flows are simulated to test the accuracy and the conservation of the FDM-FPM hybrid approach. The standing waves and flows around NACA airfoils are further simulated to test the ability to deal with free surfaces and complex boundaries. The results show that FDM-FPM retains not only the high efficiency of FDM with multiple resolutions but also the ability of FPM in modeling free surfaces and complex boundaries.     

Effect of rock shapes on brittle fracture using Smoothed Particle Hydrodynamics

Breakage of rocks or particulates plays a major role in various industries, such as mineral and ore processing. Many of the processes used for fracturing materials in these industries have the requirement to produce specified size and/or shape of the products. Numerical modelling can assist in understanding and predicting complex fracture processes, and can be used in designing the equipment and setting the process parameters to ensure desired product quality. In this paper, a mesh-free numerical method, called Smoothed Particle Hydrodynamics (SPH), is extended to predict impact fracture of rocks. SPH is a particle based Lagrangian method which is particularly suited to the analysis of fracture due to its capacity to model large deformation and track the free surfaces generated. A continuum damage model is used to predict the fracture of rocks. Evolution of damage is predicted using the strain history of each particle. Damage inhibits the transmission of tensile stress between particles, and once it reaches unity, the particle is unable to transmit tensile stress, resulting in a macro-crack. Connected macro-cracks lead to complete fragmentation.Firstly, an Unconfined Compressive Strength (UCS) test under uniaxial compression of a rock sample is modelled using SPH and compared against experiments to validate the capability of SPH for prediction of fracture in rocks. The SPH prediction matched the well-known experimentally observed diagonal fracture pattern. SPH is subsequently used to simulate brittle fracture of rocks during impact. Rock specimens of different shapes are examined to determine the effects of shape on both the fracture pattern and the energy dissipation during impact fracture. Rock shape is found to have considerable influence on the fracture process, fragment sizes, energy dissipation, and post-fracture motion of the fragments.     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.