基于SPH方法的滴水涟漪动画模拟

光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)方法是一种新近发展的可用于流体模拟的无网格数值方法.文中基于SPH方法的基本原理,利用SPH方法求解描述水流现象的二维浅水波方程,根据具体模型使用Monaghan人工粘性的变形形式,有效地防止了相互靠近粒子的穿透,消除了SPH方法在模拟流体动力学问题时产生的数值振荡.通过使用可变光滑长度,使邻近粒子的数量保持相对稳定,提高了求解的计算效率和精度.同时,对光滑长度进行了修正以获取对称光滑长度,保持了粒子间相互作用对称性.全面考虑了各种定解条件的设置,对水滴的运动进行了模拟,SPH模拟结果与有限差分法、有限体积法结果非常吻合,验证了方法的准确性,为SPH方法的进一步发展和广泛运用奠定了基础.     

基于光滑粒子动力学方法的爆轰波对碰实验数值仿真

为分析爆轰波对碰实验及不同材料飞层在爆轰波对碰作用下的动力学响应,采用能处理断裂和复杂界面的光滑粒子动力学(Smoothed Particle Hydrodynamics,SPH)方法进行数值模拟.采用二维轴对称SPH离散形式,光滑函数采用B-样条函数;利用二维流体动力学程序进行数值模拟.数值模拟结果与实验结果符合较好...     

一种基于自适应光滑长度的SPH液体模拟方法

传统SPH流体模拟方法通常使用固定的粒子光滑长度进行插值计算,在某些情况下会导致较大的插值误差。为提升模拟精度,建立了粒子光滑长度与邻居粒子密度调和平均数间的关系,自适应调整粒子的光滑长度,并设计和定义了相应的邻居搜索方案和核函数以解决受力不对称的问题。经实验验证,粒子邻居数方差有效降低,解决了传统SPH支持域固定导致的粒子插值误差过大的问题,使仿真结果更接近物理事实。同时由于物理计算精度的提高,模拟稳定性得到增强,可使用更大的时间步长,有效提升了模拟速度。最终,相比其他方法在视觉质量和模拟速度上均具有一定优势。     

储箱内液体晃动动力学分析及防晃结构优化

基于光滑粒子流体动力学( SPH)方法对无阻尼板和装有阻尼板的矩形储箱在加速度激励作用下,储箱内液体的晃动与冲击进行了三维数值模拟,将测试点的计算压力及液体晃动模拟与试验进行了对比,吻合较好.从而验证了SPH方法在求解具有强非线性液体大幅晃动问题方面的准确性和优越性.分析表明:阻尼板的安装对液体的晃动特性具有显著的影响...     

SPH方法核近似形式改进及算法研究

光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)方法是一种无网格拉格朗日粒子法,目前在流体力学领域以及大变形和冲击载荷等问题的模拟方面具有广泛的应用,众多学者在SPH算法方面开展了大量的研究,以提高SPH算法的计算速度和精度.针对现有SPH方法在边界附近粒子近似精度下降的问题,本文在CSPH方法和MSPH方法基础上提出了一种改进的核近似形式,在求解场函数、一阶导数近似值以及二阶导数近似值过程中,对含二阶导数项的方程进行优化,减少了二阶导数项近似值的求解个数,相比MSPH方法减少了计算量.此外,本文基于改进的SPH算法,建立了二维数值波浪水槽模拟推板造波,通过数值模拟造波将SPH算法生成的波浪参数与理论值进行对比,验证了改进的SPH方法在波浪生成和传播上具有较好的模拟效果,为后续研究内波、畸形波以及非线性波相互作用提供了算法研究基础.     

SPH法中初始时粒子配置的分析

光滑粒子流体动力学（SPH）法是一种无网格拉格朗日粒子法。文中介绍了SPH法的常数和线性连续性条件,测试求解一维溃坝问题时不同的初始粒子配置对实验结果的影响。结果表明在SPH法中,初始时刻粒子应尽量均匀分布,并且尽量使所有粒子的质量相同或者是呈连续变化的。     

SPH法中初始时粒子配置的分析

光滑粒子流体动力学(SPH)法是一种无网格拉格朗日粒子法。文中介绍了SPH法的常数和线性连续性条件,测试求解一维溃坝问题时不同的初始粒子配置对实验结果的影响。结果表明在SPH法中,初始时刻粒子应尽量均匀分布,并且尽量使所有粒子的质量相同或者是呈连续变化的。     

几种溃坝问题的SPH方法数值模拟

光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)法是近二十年来发展起来的一种纯的拉格朗日无网格粒子方法.由于它计算空间导数时不需要使用网格并且具有自适应性质,从而避免了高维拉氏网格法中的网格缠结和扭曲的麻烦,被广泛地应用到了各种领域.通过介绍SPH方法并结合浅水波方程,引入处理边界问题常用的虚粒子方法.利用SPH方法结合虚粒子的方式讨论了对于溃坝问题中常见的漂浮物和障碍物的模拟,并通过数值实验的方式证明了此方法在模拟复杂流体运动上的可行性,为SPH方法的进一步发展和广泛应用奠定了基础.     

基于粒子分解的SPH并行算法研究与应用

作为一种典型的拉格朗日型无网格数值方法,光滑粒子流体动力学（SPH）方法在模拟自由表面流问题时具有天然优势。但是,该方法计算量大、耗时长,为此提出了一种基于粒子分解的SPH并行算法。该算法将所有粒子平均分配到各个进程进行计算,每个时间步通信仅调用一次发送、接收和广播函数,因此易于实现且可扩展性较好。应用该并行算法对二维溃坝流和三维液滴冲击液膜问题进行数值模拟,结果表明：该并行算法能显著减少模拟所消耗的计算时间,有利于进行三维大规模计算问题的数值模拟;当粒子数大于百万时,最大加速比可达30以上。     

基于ARM SVE的光滑粒子流体动力学SIMD加速方法

光滑粒子流体动力学（SPH）是近年来兴起的一种无网格的粒子方法,SPH在处理大变形、运动物质表面以及自由表面等问题时优势明显,在数值模拟领域得到了非常广泛的应用,是一种典型的科学计算应用。作为一种显式的粒子方法,SPH在每一个迭代步都需要计算大量的粒子间相互作用,计算量非常大,如何提高SPH的计算效率成为研究热点。可伸缩矢量扩展（SVE）是ARM针对高性能计算推出的下一代SIMD指令集,基于SVE研究了SPH方法的SIMD加速方法,取得了显著的加速效果。     

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.     

Smoothed particle hydrodynamics: Applications to heat conduction

In this paper, we modify the numerical steps involved in a smoothed particle hydrodynamics (SPH) simulation. Specifically, the second order partial differential equation (PDE) is decomposed into two first order PDEs. Using the ghost particle method, consistent estimation of near-boundary corrections for system variables is also accomplished. Here, we focus on SPH equations for heat conduction to verify our numerical scheme. Each particle carries a physical entity (here, this entity is temperature) and transfers it to neighboring particles, thus exhibiting the mesh-less nature of the SPH framework, which is potentially applicable to complex geometries and nanoscale heat transfer. We demonstrate here only 1D and 2D simulations because 3D codes are as simple to generate as 1D codes in the SPH framework. Our methodology can be extended to systems where the governing equations are described by PDEs.     

基于SPH与FEM的结构入水分析方法

建立基于光滑粒子动力学（smoothed particle hydrodynamics, SPH）、有限元法（finite element method, FEM）和无反射边界耦合的结构入水分析方法,将无限水域利用无反射边界条件截断成有限水域,将有限水域分为流体变形大的SPH区域、流体变形小的FEM区域和声学流体FEM区域,结构用FEM离散。采用通用接触算法模拟SPH与FEM的耦合,采用声固耦合方法处理FEM区域之间的耦合,建立流固耦合的SPH FEM分析方法。该方法结合SPH模拟大变形的优点和FEM的高效性,可实现含自由液面变形、液体飞溅和无限水域等特点的流固耦合问题的模拟,为结构入水分析缩小离散区域、降低自由度和SPH粒子数等提供一种有效的分析方法。     

A GPU-accelerated smoothed particle hydrodynamics (SPH) model for the shallow water equations

Smoothed particle hydrodynamics (SPH) is a fully Lagrangian meshless computational method for solving the fluid dynamics equations. In recent years, it has also been employed to solve the shallow water equations (SWEs) and promising results have been obtained. However, SPH models are computationally very demanding and the SPH-SWE models considered in this work have no exception. In this paper, the Graphic Processing Units (GPUs) are explored to accelerate an SPH-SWE model for wider applications. Unlike Central Processing Units (CPUs), GPUs are highly parallelized, which makes it suitable for accelerating scientific computing algorithms like SPH. The aim is to design a GPU-based SPH model for solving the two-dimensional SWEs with variable smoothing lengths. Furthermore, a quad-tree neighbour searching method is implemented to further optimize the model performance. An idealized benchmark test and two real-world dam-break cases have been simulated to demonstrate the superior performance of the current GPU-accelerated high-performance SPH-SWE model.     

Turbulent Details Simulation for SPH Fluids via Vorticity Refinement

A major issue in smoothed particle hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High‐frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a vorticity refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot‐Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods.     

The simulation of some chemotactic bacteria patterns in liquid medium which arises in tumor growth with blow-up phenomena via a generalized smoothed particle hydrodynamics (GSPH) method

In the recent decades, the biological models have been noticed to find a suitable numerical procedure. Among the biological models, equations in tumor growth have many applications. In the current paper, we consider some equations in chemotaxis and haptotaxis models. The studied models have blow-up phenomena in their solutions. In addition, the proposed numerical technique is based on a meshless method that is well-known generalized smoothed particle hydrodynamics (SPH) method.

     

A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems

In this work, a mixed corrected symmetric smoothed particle hydrodynamics (MC-SSPH) method is proposed for solving the non-linear dynamic problems, and is extended to simulate the fluid dynamic problems. The proposed method is achieved by improving the conventional SPH, in which the constructed process is based on decomposing the high-order partial differential equation into multi-first-order partial differential equations (PDEs), correcting the particle approximations of the kernel and first-order kernel gradient of SPH under the concept of Taylor series, and finally making the obtained local matrix symmetric. For the purpose of verifying the validity and capacity of the proposed method, the Burgers? and modified KdV–Burgers? equations are solved using MC-SSPH and compared with other mesh-free methods. Meanwhile, the proposed MC-SSPH is further extended and applied to simulate free surface flows for better illustrating the special merit of particle method. All the numerical results agree well with available data, and demonstrate that the MC-SSPH method possesses the higher accuracy and better stability than the conventional SPH method, and the better flexibility and extended application than the other mesh-free methods.     

Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology

In this paper, the smoothed particle hydrodynamics (SPH) is applied to simulate the high explosive (HE) explosion which consists of detonation and dispersion process. The combination of meshless and Lagrangian nature inherent in the SPH methodology avoids the disadvantages of traditional numerical methods in treating large deformations, large inhomogeneities and tracing free surfaces in the extremely transient explosion process. Four numerical examples are presented with comparisons from different sources. The presented numerical examples involve in various HE explosion scenarios of arbitrary charge shape and different detonation orientations. The simulation results show that the presented SPH methodology can give good prediction for both the magnitude and form of the detonation wave as well as the pressure transient in the explosion process. Major physics of the HE explosion can be well captured in the simulation.     

Numerical simulation of fluid–structure interaction by SPH

A Lagrangian model for the numerical simulation of fluid–structure interaction problems is proposed in the present paper. In the method both fluid and solid phases are described by smoothing particle hydrodynamics: fluid dynamics is studied in the inviscid approximation, while solid dynamics is simulated through an incremental hypoelastic relation. The interface condition between fluid and solid is enforced by a suitable term, obtained by an approximate SPH evaluation of a surface integral of fluid pressure.The method is validated by comparing numerical results with laboratory experiments where an elastic plate is deformed under the effect of a rapidly varying fluid flow.     

A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics

We present a novel smoothed particle hydrodynamics (SPH) method for diffusion equations subject to Neumann and Robin boundary conditions. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to implement in numerical methods when the boundary geometry is complex. The new method presented here is based on the approximation of the sharp boundary with a diffuse interface and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method. The paper discusses the details of the method and the criteria for the width of the diffuse interface. The method is used to simulate diffusion and reactions in a domain bounded by two concentric circles and reactive flow between two parallel plates and its accuracy is demonstrated through comparison with analytical and finite difference solutions. To further illustrate the capabilities of the model, a reactive flow in a porous medium was simulated and good convergence properties of the model are demonstrated.