A splitting scheme for highly dissipative smoothed particle dynamics

Smoothed particle dynamics refers to Smoothed Particle Hydrodynamics (SPH) when simulating macroscopic flows and to Smoothed Dissipative Particle Dynamics (SDPD) when simulating mesoscopic flows. When the considered flow is highly dissipative, this otherwise very attractive method faces a serious time-step limitation. This difficulty, known in literature as Schmidt number problem for Dissipative Particle Dynamics (DPD), prevents the application of SDPD for important cases of liquid micro-flows. In this paper we propose a splitting scheme which allows to increase significantly the admissible time-step size for SPH and SDPD. Macroscopic and mesoscopic validation cases, and numerical simulations of polymer in shear flows suggest that this scheme is stable and accurate, and therefore efficient simulations at Schmidt numbers of order O(10⁶) are possible.     

Dynamical regimes in the dissipative particle dynamics model

We discuss theoretically the behavior of the velocity autocorrelation function in the dissipative particle dynamics (DPD) model. Two dynamical regimes are identified depending on the dimensionless model parameters. For low values of the dimensional friction, a mean field behavior is observed in which the kinetic theory for the DPD model provides good predictions. For high values of the friction, collective hydrodynamic effects are dominant. We have performed numerical simulations that validate the theory presented.     

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。     

非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟

为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性.同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型.通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性.随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.     

Controlling density fluctuations in wall-bounded dissipative particle dynamics systems

Dissipative Particle Dynamics (DPD) simulations of wall-bounded flows exhibit density fluctuations that depend strongly on the no-slip boundary condition and increase with the level of coarse graining. We develop an adaptive model for wall-particle interactions that eliminates such oscillations and can target prescribed density profiles. Comparisons are made with ideal no-slip boundary conditions and molecular dynamics simulations. The new model is general and can be used in other coarse-grained particle methods.     

Dependence of thermodynamic properties of model systems on some dissipative particle dynamics parameters

The influence of systematic perturbation of input interaction parameters on thermodynamic equilibrium properties is studied employing dissipative particle dynamics (DPD) simulations. The values of both the excess pressure and the surface tension are found to be very sensitive to the values of the soft repulsion parameter between unlike DPD particles for high values of the coarse-graining level (number of water molecules per DPD particle). For the case in which a molecular surfactant is present at the interface we have determined the dependence of these properties on the values of the parameters that characterize the bonding force between polymer beads. No significant differences were found between linear and branched surfactants.     

Effect of shear on the symmetric diblock copolymer/nanorod mixture: A dissipative particle dynamics study

The phase behaviours of a lamellar diblock copolymer/nanorod composite under steady shear are investigated using dissipative particle dynamics.We consider a wide range of nanorod concentrations,where the nanorods each have a preferential affinity to one of the blocks.Our results suggest that shear not only aligns the orientations of the diblock copolymer templates and nanorods towards flow direction,but also regulates the distribution of the nanorods within the polymer matrix.Meanwhile,the shear-induced reorientation and morphology transitions of the systems also significantly depend on the nanorod concentration.At certain nanorod concentrations,the competitions between shearinduced polymer thinning and nanorods dispersion behaviours determine the phase behaviours of the composites.For high nanorod concentrations,no morphology transition is observed,but reorientation is present,in which the sheared nanorods are arranged into hexagonal packing arrays.Additionally,the orientation behaviour of nanorods is determined directly by the applied shear,also interfered with by the shear-stretched copolymer molecules.     

微通道疏水表面滑移的耗散粒子动力学研究

了解疏水表面的滑移规律对其在流动减阻方面的应用至关重要.利用耗散粒子动力学(dissipative particle dynamics, DPD)方法研究了微通道疏水表面的滑移现象.采用固定住的粒子并配合修正的向前反弹机制,构建了DPD固体壁面边界模型,利用该边界模型模拟了平板间的Couette流动.研究结果表明,通过调整壁面与流体间排斥作用强度,壁面能实现从无滑移到滑移的转变,壁面与流体间排斥作用越强,即疏水性越强,壁面滑移越明显,并且滑移长度与接触角之间存在近似的二次函数关系.无滑移时壁面附近密度分布均匀,有滑移时壁面附近存在低密度区域,低密度区域阻碍了动量传递,致使壁面产生滑移.     

Tagged particle fluctuations in uniform shear flow

The nonlinear Boltzmann and Boltzmann-Lorentz equations are used to describe the dynamics of a tagged particle in a nonequilibrium gas. For the special case of Maxwell molecules with uniform shear flow, an exact set of equations for the average position and velocity, and their fluctuations, is obtained. The results apply for arbitrary magnitude of the shear rate and include the effects of viscous heating. A generalization of Onsager's assumption of the regression of fluctuations is found to apply for the relationship between the equations for the average dynamics and those for the time correlation functions. The connection between fluctuations and dissipation is described by the equations for the equal-time correlation function. The source term in these equations indicates that the “noise” in this nonequilibrium state is qualitatively different from that in equilibrium, or even local equilibrium. These equations are solved to determine the velocity autocorrelation function as a function of the shear rate.     

Wall shear stress around a stationary gas slug in a downward liquid flow

A single cell of the gas-liquid slug flow was studied. The flow around an immobile gas slug in a downflow of liquid and under its bottom was measured. The values of the wall shear stress and its pulsations were measured by the electrodiffusion method depending on a distance from the slug nose. It is shown that in a liquid film around a slug, turbulent pulsations are damped in comparison with a single-phase liquid flow. In the bottom part of a slug, where vortices are detached, turbulent pulsations exceed significantly the single-phase ones. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 07-08-00405a).     

Nonlinear interaction between two components of motion upon precipitation of a heavy particle in a shear flow

When heavy particles move in a shear flow, the drag depends on the Reynolds number and, hence, on the magnitude of the particle velocity relatively to the medium. This leads to a nonlinear interaction between various components of motion. For example, when a particle precipitates in a horizontal air flow with vertical shear, it also acquires horizontal motion relative to air in addition to vertical motion. These two components of motion contribute to the hydrodynamic drag coefficient by affecting the Reynolds number and thereby influence each other. Steady motion of a particle in a flow with constant vertical shear is analyzed. Dimensionless criterion of significance of the nonlinear effect under consideration is determined. It is demonstrated that this effect can be significant in the near-surface atmospheric layer in the case of storm wind.     

Time correlations and persistence probability of a Brownian particle in a shear flow

This paper presents an adaptive lag synchronization based method for simultaneous identification of topology and parameters of uncertain general complex dynamical networks with and without time delays. Based on Lyapunov stability theorem and LaSalle??s invariance principle, an adaptive controller is designed to realize lag synchronization between drive and response systems, meanwhile, identification criteria of network topology and system parameters are obtained. Numerical simulations illustrate the effectiveness of the proposed method.     

Comparison between the Boltzmann and BGK equations for uniform shear flow

The exact fourth-degree moments derived in the preceding paper from the Boltzmann equation for Maxwell molecules under uniform shear flow are compared with those obtained from the BGK and the Gaussian approximations. It is shown that the BGK results are closer to the exact ones than the Gaussian results. However, the deviations become significant as the shear rate increases.     

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.     

Orientation and dynamics of a vesicle in tank-treading motion in shear flow

Experimental results on mean inclination angle and its fluctuation due to thermal noise in tank-treading motion of a vesicle in shear flow as a function of vesicle excess area, normalized shear rate, viscosity, and viscosity contrast between inner and outer fluids, , are presented. Good quantitative agreement with theory made for was found. At the dependence is altered significantly. Dependence of the vesicle shape on shear rate is consistent with theory. A tank-treading velocity of the vesicle membrane is found to be a periodic function close to that predicted by theory.     

Critical behaviour in a model of stationary flow and supersymmetry breaking

We show, how a coupling of the conservative Langevin dynamics to an external field amounts to a partial supersymmetry breaking of the equivalent field theory. In the critical dynamics, this leads to a crossover to a non-conventional mean-field behaviour above 3 and 5 dimensions (depending on the symmetry of the coupling) in contrast to the naively expected upper critical dimension values 5 and 8, respectively.