微液滴动力学特性的耗散粒子动力学模拟

对传统的耗散粒子动力学方法进行了改进.改进的耗散粒子动力学方法采用了包含远程吸引力和近距排斥力的保守力势函数,从而使得用耗散粒子动力学方法模拟多相流动成为可能.应用改进的耗散粒子动力学方法,对微尺度下液滴的形成及液滴在微重力下的大幅度振荡变形进行了数值模拟.计算结果表明,改进的耗散粒子动力学(DPD)方法能够有效地描述微尺度下液滴的动力学特性,对研究复杂流体多相流动有着重要的意义. 关键词： 多相流 微液滴 耗散粒子动力学(DPD)方法 保守力势函数     

带凹槽的微通道中液滴运动数值模拟

运用改进的耗散粒子动力学方法模拟了液滴在由凹槽所构成的粗糙表面微通道内的运动行为.改进的耗散粒子动力学方法采用新近提出的一种短程排斥、长程吸引相互作用势能函数,从而可以模拟带有自由面的流体,如液滴等.模拟了新势能函数下液滴与固体壁面的静态接触角,并用2次多项式拟合了"接触角-a_wf/a_f"变化曲线.研究了液滴在带凹槽的微通道中运动时,微通道壁面浸润性、外场力、液滴温度对液滴流动特性的影响.研究表明壁面浸润性和外场力对液滴流动特性的影响较大,液滴温度对液滴流动特性的影响较小.研究结果对运用耗散粒子动力学方法模拟并分析微流体在复杂微通道的流动有一定的参考价值.     

带自由面流体的多体耗散粒子动力学模拟

利用多体耗散粒子动力学(MDPD)方法对介观尺度下液滴动力学进行了模拟分析,探讨了MDPD系统中液气共存界面的形成,并对表面张力进行了模拟研究,研究结果表明,MDPD方法形成的液气共存界面满足Laplace定律,通过改变不同的粒子间保守力作用参数,获得了液滴在固体壁面上不同的接触角,并研究了保守力作用参数与接触角之间的变化规律,进一步模拟了液滴在复杂微通道内的流动,研究结果有助于解释带自由面流体在粗糙表面上的运动行为。     

有压差平板微通道内电渗流动换热的介观模拟

采用能量守恒的耗散粒子动力学方法(eDPD)对平行平板微通道内的电渗流动与换热问题进行了模拟,电势分布由Poisson-Boltzmann方程描述。获得了不同电动参数下的纯电渗速度及温度分布并分别与解析解及有限元方法对比以验证正确性及精度。进一步模拟了有压差驱动下纵向电场在壁面异质电势微通道内引起的电渗微混合与对流传热问题,研究结果表明纵向电场对通道内的流动与传热具有明显的影响,而压力梯度的增大会导致电渗作用被逐渐削弱。     

微通道中高分子溶液Poiseuille流的耗散粒子动力学模拟

利用耗散粒子动力学(dissipative particle dynamics, DPD)方法模拟了微通道中高分子溶液的Poiseuille流动.研究表明, 微通道中的高分子溶液呈现非牛顿流体特性, 可以用幂律流体来描述流动行为, 高分子浓度越大, 幂律指数n 越小. 高分子链与壁面的流体动力学相互作用以及布朗扩散率梯度控制着高分子链的横向迁移. 由于传统的DPD方法中壁面诱导的流体动力学作用部分被屏蔽, 高分子链将向壁面方向迁移, 并且随着流场增强, 高分子链向壁面方向迁移越明显. 未被屏蔽的流体动力学相互作用和布朗扩散率梯度相互竞争, 使高分子链在微通道内的质心分布呈双峰状, 通道中心处高分子浓度出现局部最小值. 当通道宽度减小、强受限时, 壁面与高分子链间的流体动力学相互作用可能全部被屏蔽, 而布朗扩散运动弱, 高分子向壁面方向有微弱的迁移. 关键词： 耗散粒子动力学 高分子溶液 非牛顿流体 横向迁移     

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.     

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.     

简单剪切流条件下液滴破碎和碰撞模拟

利用耗散粒子动力学(DPD)对简单剪切流条件下液滴的破碎和碰撞分离过程进行了模拟.液滴由多颗简单的DPD粒子构成,液滴与周围流体的不互溶性由提高它们之间的保守力系数获得.通道的上下壁面沿着相反方向运动从而使流体产生简单剪切流动.计算结果表明,在简单剪切流条件下,当界面张力数超过临界界面张力数后,液滴不稳定;液滴将被拉长并破碎成数个较小的稳定的液滴.当两个液滴相互碰撞并分离的现象发生时,两个液滴的质心在速度梯度方向上的距离与整个碰撞过程相关,碰撞之后的δz值比碰撞前的δz大.     

耗散粒子动力学GPU并行计算研究

研究了耗散粒子动力学基于计算统一设备架构的图形处理器(GPU)并行计算的实施.对其中涉及的算法映射模型、Cell-List法数组的并行化更新、随机数生成、存储器访问优化、负载平衡等进行了详细的讨论.进一步模拟了Poiseuille流动和突扩突缩流动,从而验证了GPU计算结果的正确性.计算结果表明,相对于基于中央处理器的串行计算,在耗散粒子动力学中实施GPU并行计算可以获得约20倍的加速比.     

用SPH-MD耦合算法模拟微通道中的液氩流动

本文构造了SPH(光滑粒子动力学)-MD(分子动力学)耦合程序,在不同宽度微通道内,对不同驱动力下的液氩流动进行了模拟计算。结果表明,在通道宽度较窄时,流体速度分布和黏性系数分布均表现出很强的微尺度效应,随着通道宽度增大,这种微尺度效应逐渐减弱,流动特征逐渐接近于宏观Poiseuille流。     

The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection–diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations system is solved using a fractional time step procedure, splitting the convective components from the diffusive ones. In the case of existing scalar potential of the flow field, the convective components are solved using a finite volume marching in space and time (MAST) procedure; this solves a sequence of small systems of ordinary differential equations, one for each computational cell, according to the decreasing value of the scalar potential. In the case of variable-density groundwater transport problem, where a scalar potential of the flow field does not exist, a second MAST procedure has to be applied to solve again the ODEs according to the increasing value of a new function, called approximated potential. The diffusive components are solved using a standard Galerkin finite element method. The numerical scheme is validated using literature tests.     

Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces

We present a new method for computing two-dimensional Stokes flow with moving interfaces that respond elastically to stretching. The interface is moved by semi-Lagrangian contouring: a distance function is introduced on a tree of cells near the interface, transported by a semi-Lagrangian time step and then used to contour the new interface. The velocity field in a periodic box is calculated as a potential integral resulting from interfacial and body forces, using a technique based on Ewald summation with analytically derived local corrections. The interfacial stretching is found from a surprisingly natural formula. A test problem with an exact solution is constructed and used to verify the speed, accuracy and robustness of the approach.     

Four-parameter analytical local model potential for atoms

Analytical local model potential for modeling the interaction in an atom reduces the computational effort in electronic structure calculations significantly. A new four-parameter analytical local model potential is proposed for atoms Li through Lr, and the values of four parameters are shell-independent and obtained by fitting the results of X_a method. At the same time, the energy eigenvalues, the radial wave functions and the total energies of electrons are obtained by solving the radial Schr?dinger equation with a new form of potential function by Numerov's numerical method. The results show that our new form of potential function is suitable for high, medium and low Z atoms. A comparison among the new potential function and other analytical potential functions shows the greater flexibility and greater accuracy of the present new potential function.     

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel*

This paper investigates the magnetohydrodynamic (MHD) electroosmotic flow (EOF) of Newtonian fluid through a zeta potential modulated parallel plate microchannel with patterned hydrodynamic slippage. The driven mechanism of the flow originates from the Lorentz force generated by the interaction of externally imposed lateral electric field $E_y$ and vertical magnetic field $B_z$ and electric field force produced by an externally applied electric field $E_x$. It is assumed that the wall zeta potential and the slip length are periodic functions of axial coordinate $x$, an analytical solution of the stream function is achieved by utilizing the method of separation of variables and perturbation expansion. The pictures of streamlines are plotted and the vortex configurations produced in flow field due to patterned wall potential and hydrodynamic slippage are discussed. Based on the stream function, the velocity field and volume flow rate are obtained, which are greatly depend on some dimensionless parameters, such as slip length $l_s$, electrokinetic width $\lambda$, the amplitude $\delta$ of the patterned slip length, the amplitude $m$ of the modulated zeta potential and Hartmann number $Ha$. The variations of velocity and volume flow rate with these dimensionless parameters are discussed in details. These theoretical results may provide some guidance effectively operating micropump in practical nanofluidic applications.     

多段翼型位流的准确解

本文给出了求解多段翼型位流准确解的一种方法。采用求解拉普拉斯方程把多段翼型绕流区域变换成一个有限矩形域,然后把此矩形域变换成多个圆,从而通过求绕多个圆的准确位流解来求得绕多段翼型位流的准确解。本文提供的方法能广泛应用到任意外形的多段翼型位流计算。采用这种方法计算所得的位流压力分布与用其它方法求得的压力分布非常吻合。     

A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential

With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver's random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations.     

Basic function method A new numerical method on unstructured grids

A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the polynomial as basic function, applying the technique of flux splitting method and the combination of central and upwind schemes, the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-, two- and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially, combining with the adaptive remeshing technique, the satisfactory results can be obtained by these schemes.     

Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability

Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability is studied. The flow is modeled by the reduced MHD equations with constant resistivity and viscosity. For super-Alfvénic flow, localized transient reconnection is observed on the Kelvin-Helmholtz time scale (this is not new). We study this transient reconnection and consider the peak reconnection rate which occurs with the initial vortex formation. Over the range of resistivities considered, it is shown that this peak reconnection rate is not a function of resistivity, and is a function of the initial flow shear. Additionally, it is demonstrated that there is a fundamental difference between the evolution of a problem at S = 200 and S = 10,000.     

Beta function and anomaly of the Fermi surface for a d=1 system of interacting fermions in a periodic potential

We derive a perturbation theory, based on the renormalization group, for the Fermi surface of a one dimensional system of fermions in a periodic potential interacting via a short range, spin independent potential. The infrared problem is studied by writing the Schwinger functions in terms of running couplings. Their flow is described by a Beta function, whose existence and analyticity as a function of the running couplings is proved. If the fermions are spinless we prove that the Beta function is vanishing and the renormalization flow is bounded for any small interaction. If the fermions are spinning the Beta function is not vanishing but, if the conduction band is not filled or half filled and the interaction is repulsive, it is possible again to control the flow proving the partial asymptotic freedom of the theory. This is done showing that the Beta function is partially vanishing using the exact solution of the Mattis model, which is the spin analogue of the Luttinger model. In both these cases Schwinger functions are anomalous so that the system is a Luttinger liquid. Our results extend the work in [B.G.P.S.], where neither spin nor periodic potential were considered; an explicit proof of some technical results used but not explicitly proved there is also provided.