修正SPH方法在自由表面模拟中的应用

对传统光滑粒子动力学(SPH)方法进行修正,提出了一种密度初始化方法,同时采用一种新的固壁边界处理方法,模拟溃坝问题。通过液滴旋转和无透空块体溃坝问题的模拟验证了修正SPH方法的有效性和在自由表面模拟中的准确性,分析了密度初始化对流动的影响;数值结果表明,修正SPH方法提高了数值计算的精度和稳定性。最后应用修正SPH方法模拟了有透空块体和挡板紧挨水柱的溃坝现象,比较了有无透空块体两种情况下右端直墙上压力变化情况,结果表明,透空块体可使右端直墙上的压力减小,有无挡板、挡板位置和水柱长高比对溃坝现象有重要影响。     

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。     

任意多面体边界一致四面体网格生成方法

提出一种能够满足多面体边界几何与拓扑约束的边界一致恢复算法,解决了任意多面体的边界一致四面体网格生成问题。在恢复多面体的几何约束时,边界上可能会引入Steiner点,这样就不满足拓扑约束。对此,本文采用动态规划方法将Steiner点从边界上消除,修复与其相关四面体单元的拓扑关系,以保持原多面体边界的拓扑完整性,并采用扩展的Laplacian光顺算法优化劣质单元。在理论上,本文算法能够保证完整地恢复任意多面体的边界。算例表明,本文提出的边界一致恢复算法鲁棒性高,可应用于复杂多面体模型。     

一种新的准结构网格生成方法

在有限元分析中,高质量的结构网格可以有效地提高有限元分析的精度,但结构网格的几何适应性差,针对复杂边界的二维计算模型,现有的方法很难自动生成高质量的结构网格;而非结构网格几何适应性很好,但存在计算效率低和精度差等问题。提出了一种新的准结构网格生成方法,能够实现复杂区域的网格自动生成并且具有高网格质量。该方法首先对计算区域运用Delaunay三角剖分技术生成粗背景网格;然后利用背景网格,使用优化的Voronoi图生成过渡的蜂巢网格;最后,通过中心圆方法对蜂巢网格单元进行结构网格剖分。分析NACA0012翼型数值模拟结果表明,提出的新准结构网格生成方法能够对边界复杂的模型自动生成高质量的网格,并且通过三种不同拓扑类型网格计算结果相互对比及与实验结果对比,证明准结构网格具有高计算精度。     

基于三角网格动静区域分离的改进RGB-D SLAM方法（英文）

针对机器人导航中动态环境下的同时定位和建图问题,提出了一种可在动态场景下稳定实时运行的RGB-D SLAM方法。通过从静态背景中分割并剔除动态对象,并在系统RANSAC解算过程中提取静态背景中的特征点来估计相机轨迹,使得系统在动态场景下能稳健定位;对当前帧构建Delaunay三角网格,并判断当前帧与参考帧的匹配点对的距离一致性,通过删除动静状态不一致的点对线段来剔除网格中的动态物体;结合带加权的词典方法,通过减小动态物体在动态场景的权重,进一步提高系统精度。实验结果表明,所提出的方法在TUM数据集的高动态序列中准确度相比现有实时SLAM方法提高了81.37%,显著提高了移动机器人在动态场景下的定位精度。     

并行求解周期性三对角方程组的谢-莫方法

针对工程计算中出现的周期性三对角线性方程组,本文利用谢尔曼-莫里森方法修正周期性三对角线性方程组,将其转化为求解两个三对角线性方程组的问题,结合分治法进行并行计算。在对周期性三对角线性方程组并行化分析的基础上,在集群系统中利用可移植消息传递标准MPI进行并行程序设计。结果表明,使用该方法求解周期性三对角线性方程组,既具有数值稳定性,又收到较好的并行效果。     

上浮气泡与自由表面相互作用的ISPH-FVM耦合方法模拟

上浮气泡与自由表面相互作用的过程涉及复杂的界面拓扑演化,该过程一直是气泡流研究领域广为关注的问题之一.为探究上浮气泡与自由表面相互作用动力学行为,将不可压缩光滑粒子流体动力学(incompressible smooth particle hydrodynamics, ISPH)方法与有限体积法(finite volume method, FVM)相结合提出了一种ISPH-FVM耦合方法.在ISPH-FVM耦合方法中,粒子和网格之间的信息交互是通过核近似插值技术实现,并将连续表面应力模型(continuous surface stress, CSS)引入当前耦合框架中以评估相界面处表面张力效应.此外, CSS模型通过FVM网格上定义的体积分数进行离散和计算,并且网格上的体积分数是通过网格支持域内ISPH粒子的核近似插值获得的.随后,利用ISPH-FVM耦合方法模拟了平衡状态下圆形气泡振荡以及单气泡上升,并将模拟结果与其他数值方法结果进行比较,验证了当前耦合方法中表面张力模型的收敛性以及界面追踪的准确性.为测试ISPH-FVM耦合方法模拟涉及复杂拓扑变化气泡流的性能,对上浮气泡与自由表面相...     

An SPH model for free surface flows with moving rigid objects

This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier–Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid–solid interaction and the non‐slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds‐averaged Navier–Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects. Copyright © 2013 John Wiley & Sons, Ltd.     

A consistent incompressible SPH method for internal flows with fixed and moving boundaries

An improved incompressible smoothed particle hydrodynamics (ISPH) method is presented, which employs first‐order consistent discretization schemes both for the first‐order and second‐order spatial derivatives. A recently introduced wall boundary condition is implemented in the context of ISPH method, which does not rely on using dummy particles and, as a result, can be applied more efficiently and with less computational complexity. To assess the accuracy and computational efficiency of this improved ISPH method, a number of two‐dimensional incompressible laminar internal flow benchmark problems are solved and the results are compared with available analytical solutions and numerical data. It is shown that using smaller smoothing lengths, the proposed method can provide desirable accuracies with relatively less computational cost for two‐dimensional problems. Copyright © 2015 John Wiley & Sons, Ltd.     

A coupled WC-TL SPH method for simulation of hydroelastic problems

A coupled weakly compressible (WC) and total Lagrangian (TL) smoothed particle hydrodynamics (SPH) method is developed for simulating hydroelastic problems. The fluid phase is simulated using WCSPH method, while the structural dynamics are solved using TLSPH method. Fluid and solid components of the method are validated separately. A sloshing water tank problem is solved to test the WCSPH method while oscillation of a thin plate and large deformation of a cantilever beam are simulated to test the TLSPH method. After validating each component, the coupled WC-TL SPH scheme is used to simulate two benchmark hydroelastic problems. The first test case shows the evolution of water column with an elastic boundary gate, and the second one investigates the breaking water column impact on elastic structures. The agreement between WC-TL SPH results and literature data shows the ability of the proposed method in simulating hydroelastic phenomena.     

An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF‐SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF‐SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF‐SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF‐SPH method avoids nested approximation of first order derivatives, and keeps the good feature of ‘kernel gradient free’. The two‐dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF‐SPH and improved KGF‐SPH. The numerical results show that the improved KGF‐SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF‐SPH. Copyright © 2015 John Wiley & Sons, Ltd.     

Conservation of circulation in SPH for 2D free‐surface flows

In this paper, we study how accurately the Smoothed Particle Hydrodynamics (SPH) scheme accounts for the conservation and the generation of vorticity and circulation, in a low viscosity, weakly compressible, barotropic fluid in the context of free‐surface flows. We consider a number of simple examples to clarify the processes involved and the accuracy of the simulations. The first example is a differentially rotating fluid where the integration path for the circulation becomes progressively more complicated, whereas the structure of the velocity field remains simple. The second example is the collision of two rectangular regions of fluid. We show that SPH accurately predicts the time variation of the circulation as well as the total vorticity for selected domains advected by the fluid. Finally, a breaking wave is considered. For such a problem we show how the dynamics of the vorticity generated by the breaking process is captured by the SPH model. Copyright © 2012 John Wiley & Sons, Ltd.     

Completeness,conservation and error in SPH for fluids

Smoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ensuring completeness conditions (low‐order polynomials are interpolated exactly) are enforced when estimating property gradients, but the consequences on errors have not been investigated. Here, we present an expression for the error in an SPH estimate, accounting for completeness, an expression that applies to SPH generally. We revisit the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. We find that a common method for enforcing completeness violates a property required of the kernel gradients, namely that gradients with respect the two position variables be equal and opposite. In such models this means conservation principles are not enforced and we present results that show this. As an aside we show the summation interpolant for density is a solution of, and may be used in the place of, the discretized, symmetrized continuity equation. Finally, we examine two examples of discretization errors, namely numerical boundary layers and the existence of crystallized states. Copyright © 2007 John Wiley & Sons, Ltd.     

Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method

This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.     

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.     

A kernel gradient free (KGF) SPH method

The finite particle method (FPM) is a modified SPH method with high order accuracy while retaining the advantages of SPH in modeling problems with free surfaces, moving interfaces, and large deformations. In both SPH and FPM, kernel gradient is necessary in kernel and particle approximation of a field function and its derivatives. In this paper, a new FPM is presented, which only involves kernel function itself in kernel and particle approximation. The kernel gradient is not necessary in the whole computation, and this approach is thus referred to as a kernel gradient free (KGF) SPH method. This is helpful when a kernel function is not differentiable or the resultant kernel gradient is not sufficiently smooth, and thus it is more general in selecting a kernel function. Moreover, different from the original FPM with an asymmetric corrective matrix, in the new FPM, the resultant corrective matrix is symmetric, and this is advantageous in particle approximations. A series of numerical examples have been conducted to show the efficiencies of KGF‐SPH including one‐dimensional mathematical tests of polynomial functions with equal or variable smoothing length and two‐dimensional incompressible fluid flow of shear cavity. It is found that KGF‐SPH is comparable with FPM in accuracy and is flexible as SPH. Copyright © 2015 John Wiley & Sons, Ltd.