粒子法中压力振荡的机理研究

移动粒子半隐式法(moving particle semi-implicit method, MPS)是一种适用于不可压缩流体的无网格方法, MPS方法常应用于自由表面大变形问题.MPS 方法提出至今一直存在着严重的压力振荡问题. 本研究针对MPS 方法中存在的压力振荡现象, 首先将实际的物理问题简化为一维模型, 并从粒子之间相互位置关系的角度说明了MPS 方法中压力波动产生的原因.在采用MPS方法进行模拟时, 加入了粒子碰撞模型, 通过对碰撞系数的选择从而控制粒子之间的相互位置关系.并且对经典的溃坝问题进行了模拟, 结果表明随着碰撞系数的增加, 粒子数密度偏差的波动幅度都会减小, 从而压力振荡的幅度得到了有效的抑制.并且对比了两种不同核函数对压力振荡的影响, 结果表明: 采用高斯核函数时, 压力振荡的幅度更小, 这是因为采用高斯核函数时, 相同的粒子位置波动幅度将会得到较小的粒子数密度偏差的波动.由于在模拟过程中粒子运动的随机性, 这将导致粒子数密度偏差产生随机的波动, 从而产生压力振荡, 因此粒子法中的压力振荡很难彻底消除.      

粒子法中压力振荡的机理研究

移动粒子半隐式法(moving particle semi-implicit method,MPS)是一种适用于不可压缩流体的无网格方法,MPS方法常应用于自由表面大变形问题.MPS方法提出至今一直存在着严重的压力振荡问题.本研究针对MPS方法中存在的压力振荡现象,首先将实际的物理问题简化为一维模型,并从粒子之间相互位置关系的角度说明了MPS方法中压力波动产生的原因.在采用MPS方法进行模拟时,加入了粒子碰撞模型,通过对碰撞系数的选择从而控制粒子之间的相互位置关系.并且对经典的溃坝问题进行了模拟,结果表明随着碰撞系数的增加,粒子数密度偏差的波动幅度都会减小,从而压力振荡的幅度得到了有效的抑制.并且对比了两种不同核函数对压力振荡的影响,结果表明:采用高斯核函数时,压力振荡的幅度更小,这是因为采用高斯核函数时,相同的粒子位置波动幅度将会得到较小的粒子数密度偏差的波动.由于在模拟过程中粒子运动的随机性,这将导致粒子数密度偏差产生随机的波动,从而产生压力振荡,因此粒子法中的压力振荡很难彻底消除.     

MPS与GPU结合数值模拟LNG液舱晃荡

液舱晃荡是一种在外部激励作用下部分装载的液舱内液体的波动现象,它会对液舱结构强度和运输船舶稳性产生危害.移动粒子半隐式法(moving particle semi-implicit,MPS)是一种典型的无网格粒子类方法,可以有效地模拟剧烈的液舱晃荡问题.但MPS方法存在计算效率低的缺点,难以模拟大规模三维问题,而GPU并行加速技术已广泛应用于科学计算领域.因此,本文将MPS方法与GPU并行加速技术相结合,采用CUDA程序语言编写,自主开发了MPSGPU-SJTU求解器,对三维液化天然气(liquefiednatural gas, LNG)型液舱晃荡进行了数值模拟.通过三种不同粒子间距的数值模拟,验证了求解器的收敛性,其中最大计算粒子数达到了200多万.与其他研究结果相比,MPSGPU-SJTU求解器能够准确地预测壁面砰击压力,并且捕捉晃荡过程中自由面的大幅度变形和强非线性破碎现象.相比CPU求解器的计算时间,GPU并行加速技术可以大幅度地减小计算时长,提高MPS方法的计算效率.本文将LNG型液舱与方型液舱的晃荡进行对比,结果表明在高充液率下LNG型液舱可以有效地减小晃荡幅值和壁面砰击压力.但在中低充液率下,LNG型液舱则会加剧晃荡,自由面呈现明显的三维特征.本文还进一步研究了水和LNG两种不同介质的液舱晃荡现象,数值模拟结果表明二者的流场基本相似,砰击压力则正比于液体密度.      

人工黏性增强三维移动粒子半隐算法稳定性

通过综合比较移动粒子半隐方法(moving-particle semi-implicitmethod, MPS)各种稳定性计算方法, 考虑了多种可能导致计算不稳定的因素, 并首次提出加入人工黏性来抑制非物理压力振荡, 得到了较为稳定的三维MPS算法.采用各种稳定性方案对比模拟了三维立方流体旋转状态下的变形及三维静水压问题, 并进一步与商业软件的流体体积函数方法(volumeof fluid, VOF)模型计算结果对比, 验证了其正确性.结果表明:对三维情形, 单纯应用已有的稳定性算法仍难以满足MPS计算稳定性的要求, 而进一步辅以该文提出的人工黏性方法则可以在准确性及稳定性方面均取得较好的效果, 且计算结果显示, 通过该文提出的开关模式增加人工黏性并不影响压强泊松方程的求解精度, 因而不会对流场的求解产生负面作用.     

一种SPH应力修正算法及自由表面流中的应用

提出了一种SPH应力修正算法,即模型中的拉应力和压应力分别采用不同的插值核函数和状态方程来处理,改善应力稳定性问题。介绍了一种改进的Quintic核函数,用于改善模型中压应力的稳定性。通过增加钟型核函数的光滑长度,改善模型中拉应力的稳定性。采用该应力修正算法模拟了无重力条件下方形液滴的震荡变形过程,对比分析了不同算法的模拟结果。此外,为进一步验证算法的适用性,模拟了溃坝算例。研究表明,改进的Quintic型核函数明显改善了粒子聚集现象,该SPH应力修正方法可以使液滴具有更均匀的粒子分布以及更光滑的自由表面,有效改善了SPH方法中的压应力不稳定作用以及自由表面流的模拟精度。     

基于移动粒子半隐式法的表面张力模拟

采用移动粒子半隐式法(MPS)模拟了受表面张力影响的自由面流动。表面张力的计算采取了一种较适合于MPS方法的表面自由能模型。方形液滴振荡和射流断裂的模拟结果分别与理论分析和试验结果一致,同时进行了三维射流注水模拟,从而验证了MPS方法结合该表面张力模型可以有效、方便地进行自由面流动中表面张力现象的模拟。     

基于拉氏变换的弹性动力学插值型重构核粒子法

插值型重构核粒子法的形函数具有离散点插值特性和不低于核函数的高阶光滑性,因而不仅可以直接施加本质边界条件,同时也保证了较高的计算精度．本文将弹性动力学方程作拉氏变换后,在变换域内用插值型重构核粒子法求解,最后再借助Durbin数值反演方法求得时间域的解．针对典型的弹性动力学问题,给出了插值型重构核粒子法的数值算例,并验证了本文方法的有效性．     

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...     

势问题的重构核粒子边界无单元法

将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性和正确性. }      

二维空间中基于黎曼解的SPH方法

应用传统的光滑粒子流体动力学(SPH)方法模拟激波问题能自主捕获波阵面,但是在接触间断界面处却不可避免地存在压力振荡。采用黎曼解修正粒子对之间的相互作用,并将基于黎曼解的SPH方法扩展到二维空间。通过对一维具有解析解的激波管问题和二维拟内爆问题的模拟,比较了基于黎曼解的SPH方法和传统的SPH方法。数值结果表明,相对于传统的SPH方法,基于黎曼解的SPH方法能够有效避免接触界面处的压力振荡,提高求解的精度。     

A moving particle semi‐implicit method for free surface flow: Improvement in inter‐particle force stabilization and consistency restoring

The moving particle semi‐implicit (MPS) method has been widely applied in free surface flows. However, the implementation of MPS remains limited because of compressive instability occurred when the particles are under compressive stress states. This study proposed an inter‐particle force stabilization and consistency restoring MPS (IFS‐CR‐MPS) method to overcome this numerical instability. For inter‐particle force stabilization, a hyperbolic‐shaped quintic kernel function is developed with a non‐negative and smooth second order derivative to satisfy the stability criterion under compressive stress state. Then, a contrastive study is conducted on the contradiction between the common understanding of the conventional MPS hyperbolic‐shaped kernel function and its performance. The result shows that the conventional MPS hyperbolic‐shaped kernel function can easily cause violent repulsive inter‐particle force and then lead to the compressive instability. Therefore, the first order derivative of the modified hyperbolic‐shaped quintic kernel function is recommended as the form of the contribution of the neighbor particles to achieve a more stable inter‐particle repulsive force. For consistency restoring, the Taylor series expansion and the hyperbolic‐shaped quintic kernel are combined to improve the accuracy of the viscosity and pressure calculation. The IFS‐CR‐MPS algorithm is subsequently verified by the inviscid hydrostatic pressure, jet impacting, and viscous droplet impacting problems. These results can be used for choosing kernel function and the contribution of neighbor particles in particle methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved MPS method with variable‐size particles

Using variable‐size particles in the moving particle semi‐implicit method (MPS) could lead to inaccurate predictions and/or numerical instability. In this paper, a variable‐size particle moving particle semi‐implicit method (VSP‐MPS) scheme is proposed for the MPS method to achieve more reliable simulations with variable‐size particles. To improve stability and accuracy, a new gradient model is developed based on a previously developed MPS scheme that requires no surface detection MPS. The dynamic particle coalescing and splitting algorithm is revised to achieve dynamic multi‐resolution. A cubic spline function with additional function is employed as the kernel function. The effectiveness of the VSP‐MPS method is demonstrated by three verification examples, that is, a hydrostatic pressure problem, a complicated free surface flow problem with large deformation, and a dynamic impact problem. The new VSP‐MPS scheme with variable‐size particles is found to have balanced efficiency and accuracy that is suitable for simulating large systems with complex flow patterns. Copyright © 2015 John Wiley & Sons, Ltd.     

Improvement of stability in moving particle semi‐implicit method

Moving particle semi‐implicit (MPS) method is one of the particle methods, which can be used to analyze incompressible free surface flow without surface tracking by a mesh or a scalar quantity. However, MPS causes unphysical numerical oscillation of pressure with high frequencies. We proposed a new formulation for the source term of Poisson equation of pressure. The proposed source term consists of three parts, one main part and two error‐compensating parts. With proper selection of the coefficients for the error‐compensating parts, we can suppress the unphysical pressure oscillation. Smoother pressure distributions are obtained in hydrostatic pressure and dam break problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.     

A one-dimensional meshfree particle formulation for simulating shock waves

In this paper, a one-dimensional meshfree particle formulation is proposed for simulating shock waves, which are associated with discontinuous phenomena. This new formulation is based on Taylor series expansion in the piecewise continuous regions on both sides of a discontinuity. The new formulation inherits the meshfree Lagrangian and particle nature of SPH, and is a natural extension and improvement on the traditional SPH method and the recently proposed corrective smoothed particle method (CSPM). The formulation is consistent even in the discontinuous regions. The resultant kernel and particle approximations consist of a primary part similar to that in CSPM, and a corrective part derived from the discontinuity. A numerical study is carried out to examine the performance of the formulation. The results show that the new formulation not only remedies the boundary deficiency problem but also simulates the discontinuity well. The formulation is applied to simulate the shock tube problem and a 1-D TNT slab detonation. It is found that the proposed formulation captures the shock wave at comparatively lower particle resolution. These preliminary numerical tests suggest that the new meshfree particle formulation is attractive in simulating hydrodynamic problems with discontinuities such as shocks waves.Received: 8 October 2002, Accepted: 10 May 2003, Published online: 15 August 2003     

MPS-FEM数值分析带自由面的流固耦合问题

随着计算科学的发展,研究人员为探索流固耦合问题的物理机理而提出了众多的数值方法。其中,耦合的移动粒子半隐式方法 MPS(Moving Particle Semi-Implicit method)和有限单元法FEM(Finite Element method)为流固耦合问题的数值仿真工作提供了新的途径。本文所有流场的数值模拟工作均采用课题组自主开发的无网格法求解器MLParticle-SJTU来完成。该求解器在原始的MPS法基础上,对核函数、压力梯度模型、压力泊松方程的求解和自由面判断方式等方面进行了改进。此外,在该求解器框架内,基于FEM法拓展了针对结构场进行求解的功能。首先,对MPS和FEM方法的理论模型及其耦合策略进行了介绍。然后,采用该自研MPS-FEM耦合求解器,数值模拟了溃坝流动对弹性结构的冲击及其相互作用的标准问题。通过将结构变形及自由面波型变化等结果与已发表结果进行对比,验证了该求解器在处理带自由面剧烈变化的粘性流体和柔性变形结构的耦合作用问题上的可行性。     

一种基于训练数据的迭代改进核函数

To improve performance of a support vector regression, a new method for a modified kernel function is proposed. In this method, information of all samples is included in the kernel function with conformal mapping. Thus the kernel function is data-dependent. With a random initial parameter, the kernel function is modified repeatedly until a satisfactory result is achieved. Compared with the conventional model, the improved approach does not need to select parameters of the kernel function. Sim- ulation is carried out for the one-dimension continuous function and a case of strong earthquakes. The results show that the improved approach has better learning ability and forecasting precision than the traditional model. With the increase of the iteration number, the figure of merit decreases and converges. The speed of convergence depends on the parameters used in the algorithm.