液滴在气固交界面变形移动问题的光滑粒子流体动力学模拟

为准确模拟液滴在气固交界面变形移动问题,对基于连续表面张力模型的表面张力光滑粒子流体动力学方法进行了改进.改进方法采用新的边界处理方式和界面法向修正方法,即将固体边界虚粒子色函数值根据液面的位置进行相应设定以保证气-液-固三相交界处流体粒子的界面法向沿接触线法线方向,引入Brackbill提出的壁面附着力边界条件处理方法,对在气-液-固三相交界处的流体粒子及部分固体边界虚粒子的界面法向进行修正,修正前后保持法向模值不变,得到了含壁面附着力边界条件的表面张力算法.模拟了受壁面附着力影响的水槽中液面的变化过程、液滴润湿壁面过程和剪切气流驱动液滴在固体表面变形脱落过程,并与流体体积函数方法进行了对比.结果表明,该方法在处理壁面附着力问题时精度较高,稳定性较好,适合处理工程中液滴在气固交界面变形移动问题.     

耗散粒子动力学中施加无滑移边界条件的新方法

在耗散粒子动力学(DPD)中施加无滑移边界条件是较困难的,本文提出了一种新的处理方法来实现无滑移边界条件.通过选取合适的壁面与流体粒子之间的保守力系数可以控制近壁面区的粒子数,从而可以使密度波动降低至极小值,实现无滑移边界条件.通过该方法模拟泊肃叶流动求得的流体性质与通过使用Lees-Edwards边界条件模拟剪切流动所求得的流体性质一致,证明了该方法的可靠性.     

基于修正并行光滑粒子动力学方法三维变系数瞬态热传导问题的模拟

为了解决传统光滑粒子动力学(SPH)方法求解三维变系数瞬态热传导方程时出现的精度低、稳定性差和计算效率低的问题,本文首先基于Taylor展开思想拓展一阶对称SPH方法到三维热传导问题的模拟,其次引入稳定化处理的迎风思想,最后基于相邻粒子标记和MPI并行技术,结合边界处理方法得到一种能够准确、高效地求解三维变系数瞬态热传导问题的修正并行SPH方法.通过对带有Direclet和Newmann边界条件的常/变系数三维热传导方程进行模拟,并与解析解进行对比,对提出的方法的精度、收敛性及计算效率进行了分析;随后,运用提出的修正并行SPH方法对三维功能梯度材料中温度变化进行了模拟预测,并与其他数值结果做对比,准确地展现了功能梯度材料中温度变化过程.     

基于粒子模拟的磁绝缘传输线等效电容和等效电感的计算

提出了一种基于粒子模拟的磁绝缘传输线等效电容和等效电感计算方法,在层流模型得到的同轴磁绝缘传输线等效电感和等效电容理论公式中引入修正因子,对粒子模拟所得结果进行数值拟合,获得了等效电容和等效电感修正因子依赖于电压的拟合表达式,修正后的等效电容和等效电感理论公式与粒子模拟结果符合较好,所得结果可用于磁绝缘传输线的等效电路建模。     

改进粒子水平集法及其应用

针对传统粒子水平集方法的缺陷提出一种虚拟粒子对距离函数的修正方法.改进算法针对虚拟粒子与待修正网格点的各种相对位置进行误差修正,可以避免虚拟粒子在非界面法线方向移动而产生的误差.数值求解涡旋流场问题显示:改进算法的界面捕捉性能得到显著提高.在此基础上,结合投影法求解Navier-Stokes方程组,数值模拟存在高密度比(10³量级)及粘性比(10²量级)的不可压缩两相流问题(气泡上升及自由面不稳定性问题).计算结果与已有结果吻合良好,详细分析主要控制参数对瑞利-泰勒不稳定性现象的影响.     

耗散粒子动力学处理复杂固体壁面的一种有效方法

耗散粒子动力学(dissipative particle dynamics,DPD)作为一种介观尺度拉格朗日型粒子方法,已经成功地应用于微纳米流动和生化科技的研究中.复杂固体壁面的处理和壁面边界条件的实施一直是DPD方法发展及应用的一个障碍.提出了处理复杂固体壁面的一种新的方法.复杂固体区域通过冻结随机分布并且达到平衡状态的DPD粒子代表;所冻结的DPD粒子位于临近流动区域的一个截距内;在靠近固体壁面的流动区域中设置流动反弹层,当流动DPD粒子进入此流动层后反弹回流动区域.应用这种固体壁面处理方法对简单流动区域的Poiseuille流动和复杂多孔介质内的流动进行了分析.研究表明,这种新的固体壁面处理方法能够有效模拟复杂固体区域,准确实施壁面边界条件.     

液滴冲击液膜问题的光滑粒子动力学模拟

本文对传统的光滑粒子动力学方法进行了改进．改进的光滑粒子动力学方法对传统粒子方法中的核梯度进行了修正,采用了一种新型的耦合边界条件,添加了表面张力和人工应力的计算程序．应用改进的光滑粒子动力学方法对液滴冲击液膜问题进行了数值模拟．得到了不同时刻液滴内部的压力变化特征,精细地捕捉了不同时刻的自由面,从机理上分析了液滴产生飞溅的条件,探讨了韦伯数,表面张力对液滴冲击液膜问题的影响．计算结果表明,改进光滑粒子动力学方法能够有效地描述液滴冲击液膜的动力学特性和自由表面变化特征,能够得到稳定精度的结果．     

瞬态热传导问题的复变量重构核粒子法

在重构核粒子法的基础上,引入复变量,讨论了复变量重构核粒子法.复变量重构核粒子法的优点是在构造形函数时采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于瞬态热传导问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,采用罚函数法引入本质边界条件,建立了瞬态热传导问题的复变量重构核粒子法,推导了相应的计算公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、精度高的优点.最后通过数值算例证明了该方法的有效性. 关键词： 重构核粒子法 复变量重构核粒子法 修正函数 瞬态热传导问题     

粒子模拟激光斜入射边界条件的处理

讨论了电磁场模拟中的非反射边界条件,详细推导了斜入射情况非反射边界条件的有限差分格式,并在粒子模拟程序LARED-P上将其实现,同时给出了激光斜入射时的数值模拟结果.     

一种新型光滑粒子动力学固壁边界施加模型

由于Lagrange粒子法的本质, 固壁边界条件的施加一直是光滑粒子动力学方法的难点之一. 本文从固壁边界的物理原理出发, 应用多层虚粒子表征固壁边界, 提出了一种新型固壁边界施加模型. 将虚粒子看作流体的扩展, 计算中虚粒子密度保持不变, 压力、速度等参数通过对流体粒子的插值获得, 虚粒子有条件的参与控制方程的计算, 对流体的密度/压力产生影响, 通过压力梯度隐式地表征壁面与流体之间的作用强度并对流体粒子施加沿壁面法线方向的斥力作用, 防止流体粒子对壁面的穿透. 数值算例测试结果表明, 与现有固壁边界施加方法相比, 本文方法更加符合流体与固壁边界作用的物理原理, 可以简单、有效地施加固壁边界条件, 方便地应用于具有复杂几何边界的问题, 获得稳定的流场形态、规则的粒子秩序及良好的速度、压力等参量的分布.     

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach     

Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method

The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503–1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710–1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.     

耗散粒子动力学对颗粒沉降问题的研究

给出了一种耗散粒子动力学方法模拟流体流动的理论及数值模型,包括控制方程组、边界条件、数值计算方法.使用耗散粒子动力学方法编程计算了颗粒在重力作用下的沉降运动,观察到颗粒的质量和所受重力对颗粒运动轨迹的影响,且颗粒质量越小,所受重力越小,颗粒运动所表现出的随机性越强烈.从而验证了所采用的数学模型、计算方法在流动数值模拟中的可行性及潜在优势.     

一种改进的光滑粒子流体动力学前处理方法

为了便于对任意边界形状的计算域快速地布置均匀粒子,提出了一种改进的光滑粒子流体动力学前处理方法.该方法是在2012年Colagrossi等提出的算法基础上进行改进后得到的.Colagrossi等提出的算法能够计算一些简单外形分布比较均匀的粒子.然而当光滑长度与初始粒子间距的比值较大时该方法在计算过程中会出现较强的数值震荡问题,收敛速度慢;而且在计算过程中可能会遭遇流体粒子穿透固体壁面的问题.本文通过引入未知因素修正的平滑粒子动力学模型来提高计算稳定性,并通过对边界附近的流体粒子施加边界力来避免流体粒子穿透固体壁面.算例验证结果表明,利用改进后的光滑粒子流体动力学前处理方法能够快速地对各种边界形状的计算域分布均匀粒子,并且避免了流体粒子穿透固体壁面的问题.     

A local energy-preserving scheme for Zakharov system

In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local timespace region which is independent of the boundary condition and more essential than the global energy conservation law.Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving(LEP) scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.     

Exact boundary conditions for the initial value problem of convex conservation laws

The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in theoretical analysis for conservation laws, but also in numerical computations for various numerical methods. For example, the initial value problem of the Burgers’ equation is one of the most popular benchmarks in testing various numerical methods. But in all the numerical tests the initial data have to be assumed that they are either periodic or having a compact support, so that periodic boundary conditions at the periodic boundaries or two constant boundary conditions at two far apart spatial artificial boundaries can be used in practical computations. In this paper for the initial value problem with any initial data we propose exact boundary conditions at two spatial artificial boundaries, which contain a finite computational domain, by using the Lax’s exact formulas for the convex conservation laws. The well-posedness of the initial-boundary problem is discussed and the finite difference schemes applied to the artificial boundary problems are described. Numerical tests with the proposed artificial boundary conditions are carried out by using the Lax–Friedrichs monotone difference schemes.     

A novel mesh regeneration algorithm for 2D FEM simulations of flows with moving boundary

A novel mesh regeneration algorithm is proposed to maintain the mesh structure during a finite element simulation of flows with moving solid boundary. With the current algorithm, a new body-fitted mesh can be efficiently constructed by solving a set of Laplace equations developed to specify the displacements of individual mesh elements. These equations are subjected to specific boundary conditions determined by the instantaneous body motion and other flow boundary conditions. The proposed mesh regeneration algorithm has been implemented on an arbitrary Lagrangian–Eulerian (ALE) framework that employs an operator-splitting technique to solve the Navier–Stokes equations. The integrated numerical scheme was validated by the numerical results of four existing problems: a flow over a backward-facing step, a uniform flow over a fixed cylinder, the vortex-induced vibration of an elastic cylinder in uniformly incident flow, and a complementary problem that compares the transient drag coefficient for a cylinder impulsively set into motion to that measured on a fixed cylinder in a starting flow. Good agreement with the numerical or experimental data in the literature was obtained and new transient flow dynamics was revealed. The scheme performance is further examined with respect to the parameter employed in the mesh regeneration algorithm.     

Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.     

The Modified Group Expansions for Construction of Solutions to the BBGKY Hierarchy

A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as well as local conservation laws. As a result, modified group expansions are proposed. On the basis of these expansions, a generalized kinetic equation for hard spheres and a generalized Bogolubov–Lenard–Balescu kinetic equation for a dense electron gas are derived within the polarization approximation.