考虑颗粒碰撞的多重Monte Carlo算法

从减少计算代价和改进碰撞算法出发, 提出了考虑颗粒碰撞的多重Monte Carlo算法, 它采用直接模拟Monte Carlo算法来考虑颗粒碰撞, 并与求解颗粒拉氏Langevin方程的Monte Carlo算法耦合起来, 跟踪比实际颗粒数目小得多的虚拟颗粒. 提出了时间步长选定标准、虚拟碰撞伙伴所在控制容积的判断准则、颗粒碰撞发生的判 断准则、虚拟碰撞伙伴的选择、基于随机碰撞角度的碰撞动力学, 构成了考虑颗粒碰撞的完整多重Monte Carlo算法. 对理想工况的细微颗粒流和粗重颗粒流进行了数值模拟, 颗粒碰撞率的模拟结果与理论分析解和DNS结果均符合很好, 颗粒场演变的细节信息, 如时间平均和特定时刻的颗粒数密度, 速度和颗粒湍动能等, 均与DNS结果符合很好. 数值模拟结果证明该算法不仅具有较低的计算代价, 而且能够达到足够的计算精度.     

Fokker-Planck方程有限解析/Monte Carlo数值模拟方法

对白噪声驱动随机系统的Fokker-Planck方程进行约化，求得约化方程的解析解，使 用局部解析解和Monte Carlo结合方法求解常系数Fokker-Planck方程，并与常系数Fokker-Planck方程的精确解 进行对比，之后求解了变驱动力系统的行为. 数值模拟结果表明，有限解析/Monte Carlo结合的方法，能成功求解一维Fokker-Planck方程，求解粒子数为10$^{5}$个，能获得 十分光滑的PDF分布曲线，计算颗粒在300个时，就能获得较好的均值. 其研究为两相 湍流PDF模型新计算方法研究提供基础.     

离散系统通用动力学方程求解算法的研究进展

离散系统中的颗粒物在凝并、破碎、冷凝/蒸发、成核、沉积等事件作用下颗粒尺度分布的时间演变由通用动力学方程所描述.该方程为一典型的部分积分微分方程,普通数值方法难以求解.本文详细介绍了求解通用动力学方程的矩方法、分区法、离散法、离散-分区法、MonteCarlo方法等几种算法的原理、优缺点和最新的研究进展,并着重介绍了MonteCarlo算法,包括基于时间驱动Monte Carlo方法、基于事件驱动MonteCarlo方法、常数目法、常体积法以及多重Monte Carlo算法.      

燃烧室两相流场亚网格燃烧模型的研究

在三维任意曲线坐标系下采用不同的亚网格燃烧模型对环形燃烧室火焰筒气液两相湍流瞬态反应流进行大涡模拟．计算中所采用的数学度模型有：k方程亚网格尺度模型估算亚网格湍流黏性；热通量辐射模型估算辐射换热，分别采用亚网格EBU燃烧模型（E-A model）、亚网格二阶矩输运方程模型（SOM）和亚网格二阶矩代数模型（SOM-A）估算化学反应速率．并在非交错网格系统下气相采用SIMPLE算法和混合差分格式求解，液相采用Lagrange处理，并用PSIC算法对其进行求解．通过实验结果和计算结果的比较，表明在三维任意曲线坐标系下对燃烧室火焰简两相湍流油雾燃烧流场进行大涡模拟，3种不同的亚网格燃烧模型都能真实反映两相湍流化学反应流流动及实际燃烧过程，而采用亚网格二阶矩输运方程模型稍优于其他两种亚网格燃烧模型．     

再入飞行器湍流尾迹流场研究

再入飞行器湍流尾迹流场状况，直接关系到飞行器的雷达散射特性。对再入飞行器湍流尾迹等离子体场理论模型，试图通过湍流模式理论来表达，即使用κ－ε－g模型方程来封闭平均化的全Navier-Stokes方程，从而准确获得流动平均场和脉动场信息。使用的N－S平均方程由质量加权平均过程产生，湍流模型方也经过可压缩性修正。真实气体效应重点考察空气处于局部热化学平衡状态。流动控制方程运用一个二阶TVD格式的有限体积法求解，以一典型小钝锥体零攻角再入飞行为例，计算了在两种高程（H－40km和H＝30km)条件下的高超声速湍流尾迹流场。获得的尾迹流场参数与流动物理状况符合，并且湍流脉动参数与已有相应的实验结果定性一致，初步证实该方法合理。     

基于优化算法的串联体系可靠度分析

结构体系的失效概率数学上可以表示为结构体系失效域上联合概率密度函数的积分，一般情况下很难直接积分求解。近几十年来，结构体系可靠度分析一直是可靠度领域的一个研究热点，人们提出许多方法，如：Monte—Carlo法、重要性抽样法与界限法和概率网络估算技术等，这些算法在求解精度、计算效率、收敛性和易使用性等方面是不同的。本文采用优化算法(改进的可行方向法、序列线性规划和序列二次规划法)进行串联体系可靠度分析，并且与其他算法(HL—RF法、Monte—Carlo法和重要性抽样法)的结果以及一些精确解进行了比较。结果表明，相对于其他算法，基于优化算法的可靠度分析适用性广，在收敛性和健实性等方面具有明显的优势。     

气固两相流中颗粒碰撞的Monte-Carlo数值模拟

利用颗粒碰撞动力学模型和颗粒几何碰撞率模型,采用Monte—Carlo算法来模拟颗粒之间碰撞,把该算法与求解雷诺应力-概率密度函数模型的有限差分-Monte Carlo算法耦合起来,对轴对称突扩通道内的两相旋流场进行了数值模拟,模拟结果表明,由于颗粒碰撞使颗粒的动能和湍动能在三个坐标方向上进行了再分配,从而导致颗粒的动能和湍动能在三个坐标方向上趋于各向同性;另外,由于颗粒碰撞破坏了颗粒-颗粒、颗粒-流体微团之间的速度关联,从而造成颗粒湍动能及两相速度脉动关联的降低。     

非正交网格控制容积法分析复杂形状池内的流动

介绍一种基于非正交网格控制容积法的数学模型，及其在圆形沉沙池流动研究中的应用．该模型求解轴对称流动的连续方程及时均Ｎ－Ｓ方程，并采用标准ｋ－ε紊流模型，模拟圆形池内的流动．由于采用非正交网格，此计算模型可精确模拟几何形状较复杂的沉沙池内的流动，利用上述模型对某实际沉沙池进行了流场计算，计算所得流场与模型试验实测值符合良好．     

高阶紧致格式求解二维粘性不可压缩复杂流场

提出了一种求解二维不可压缩复杂流场的高精度算法．控制方程为原始变量、压力Ｐｏｉｓｓｏｎ方程提法．在任意曲线坐标下，采用四阶紧致格式求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，时间推进采用交替方向隐式（ＡＤＩ）格式，在非交错网格上用松弛法求解压力Ｐｏｉｓｓｏｎ方程．对于复杂的流场，采用了区域分解方法，并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场．利用该算法计算了二维受驱空腔流动，弯管流动和垂直平板的突然起动问题．计算结果与实验结果和其他研究者的计算结果相比较吻合良好．对于平板起动流动，成功地模拟了流场中旋涡的生成以及Ｋａｒｍａｎ涡街的形成     

湍流燃烧中的概率密度函数方法

用求解速度和化学热力学参数联合概率密度函数(pdf)输运方程的方法,计算湍流燃烧问题时,湍流输运和化学反应等过程可以精确计算,无须模拟。它还可以提供比统计矩模型方法更多的信息,因此是一个很有潜力的方法。本文给出了湍流燃烧概率密度函数的输运方程,扼要地介绍了目前应用较多的随机过程模型,以及求解概率密度函数方程的Monte Carlo算法。最后引用两个例子说明概率密度函数方法的优越性。      

Simulation of bluff body stabilized flows with hybrid RANS and PDF method

The motivation of this study is to investigate the turbulence–chemistry interactions by using probability density function (PDF) method. A consistent hybrid Reynolds Averaged Navier–Stokes (RANS)/PDF method is used to simulate the turbulent non-reacting and reacting flows. The joint fluctuating velocity–frequency–composition PDF equation coupled with the Reynolds averaged density, momentum and energy equations are solved on unstructured meshes by the Lagrangian Monte Carlo (MC) method combined with the finite volume (FV) method. The simulation of the axisymmetric bluff body stabilized non-reacting flow fields is presented in this paper. The calculated length of the recirculation zone is in good agreement with the experimental data. Moreover, the significant change of the flow pattern with the increase of the jet-to-coflow momentum flux ratio is well predicted. In addition, comparisons are made between the joint PDF model and two different Reynolds stress models. The project supported by the National Natural Science Foundation of China (50506028), and Action Scheme for Invigorating Education Towards the twenty-first century.     

ADVECTION–DIFFUSION PROCESSES AND RESIDENCE TIMES IN SEMIENCLOSED MARINE BASINS

This paper addresses the problem of estimating the residence times in a marine basin of a passive constituent released in the sea. The dispersion process is described by an advection–diffusion model and the hydrodynamics is assumed to be known. We have performed the analysis of two different scenarios: (i) basins with unidirectional flows, in three space dimensions and under the rigid lid approximation, and (ii) basins with flows forced by the tide, under the shallow water approximation. Let the random variable τ be defined as the time spent in the basin by a particle released at a given point. The probability distribution of τ is obtained from the solution of the advection–diffusion problem and the residence time of a particle is defined as the mean value of τ. Two different numerical approximations have been used to solve the continuous problem: the finite volume and Monte Carlo methods. For both continuous and discrete formulations it is proved that if all the particles eventually leave the basin, then the residence time has a finite value. We present here the results obtained for two study cases: a two- dimensional basin with a steady flow and a one-dimensional channel with flow induced by the tide. The results obtained by the finite volume and Monte Carlo methods are in very good agreement for both scenarios.     

On the Computation of Compressible Turbulent Flows on Unstructured Grids

An accurate, fast, matrix-free implicit method has been developed to solve compressible turbulent How problems using the Spalart and Allmaras one equation turbulence model on unstructured meshes. The mean-flow and turbulence-model equations are decoupled in the time integration in order to facilitate the incorporation of different turbulence models and reduce memory requirements. Both mean flow and turbulent equations are integrated in time using a linearized implicit scheme. A recently developed, fast, matrix-free implicit method, GMRES+LU-SGS, is then applied to solve the resultant system of linear equations. The spatial discretization is carried out using a hybrid finite volume and finite element method, where the finite volume approximation based on a containment dual control volume rather than the more popular median-dual control volume is used to discretize the inviscid fluxes, and the finite element approximation is used to evaluate the viscous flux terms. The developed method is used to compute a variety of turbulent flow problems in both 2D and 3D. The results obtained are in good agreement with theoretical and experimental data and indicate that the present method provides an accurate, fast, and robust algorithm for computing compressible turbulent flows on unstructured meshes.     

FINITE ANALYTIC NUMERICAL SOLUTION OF NAVIER-STOKES EQUATIONS

The finite analytic method is used in the present study to calculate the turbulent flow field described with Navier-Stokes equation in body-fitted curvilinear coordinate system The finite analytic method invokes the analytic solution of governing partial differential equation in formulating the algebraic equation that relates a nodal value in an element to its neighbour nodal values according to the direction and the magnitude of convection. It is shown that the finite analytic method has good numerical stability and accuracy. The turbulent flow fields through a single and a tandem cascades of airfoil are numerically simulated by using finite analytic method respectively in this paper. The k ? ε turbulence model and wall function are employed in. the present study. The agreement of numerical solution with experiment result is quite good.     

Monte Carlo simulation of the heat flow in a dense hard sphere gas

The one-dimensional steady heat flow in a dense hard sphere gas is studied solving the Enskog equation numerically by a recently proposed DSMC-like particle scheme. The accuracy of the solutions is assessed through a comparison with solutions obtained from a semi-regular method which combines finite difference discretization with Monte Carlo quadrature techniques. It is shown that excellent agreement is found between the two numerical methods. The solutions obtained from the Enskog equation have also been found in good agreement with the results of molecular dynamics simulations.     

Buoyancy modelling with incompressible SPH for laminar and turbulent flows

This work aims to model buoyant, laminar or turbulent flows, using a two‐dimensional incompressible smoothed particle hydrodynamics model with accurate wall boundary conditions. The buoyancy effects are modelled through the Boussinesq approximation coupled to a heat equation, which makes it possible to apply an incompressible algorithm to compute the pressure field from a Poisson equation. Based on our previous work [1], we extend the unified semi‐analytical wall boundary conditions to the present model. The latter is also combined to a Reynolds‐averaged Navier–Stokes approach to treat turbulent flows. The k ? ? turbulence model is used, where buoyancy is modelled through an additional term in the k ? ? equations like in mesh‐based methods. We propose a unified framework to prescribe isothermal (Dirichlet) or to impose heat flux (Neumann) wall boundary conditions in incompressible smoothed particle hydrodynamics. To illustrate this, a theoretical case is presented (laminar heated Poiseuille flow), where excellent agreement with the theoretical solution is obtained. Several benchmark cases are then proposed: a lock‐exchange flow, two laminar and one turbulent flow in differentially heated cavities, and finally a turbulent heated Poiseuille flow. Comparisons are provided with a finite volume approach using an open‐source industrial code. Copyright © 2015 John Wiley & Sons, Ltd.     

Variance‐reduced Monte Carlo solutions of the Boltzmann equation for low‐speed gas flows: A discontinuous Galerkin formulation

We present and discuss an efficient, high‐order numerical solution method for solving the Boltzmann equation for low‐speed dilute gas flows. The method's major ingredient is a new Monte Carlo technique for evaluating the weak form of the collision integral necessary for the discontinuous Galerkin formulation used here. The Monte Carlo technique extends the variance reduction ideas first presented in Baker and Hadjiconstantinou (Phys. Fluids 2005; 17 , art. no. 051703) and makes evaluation of the weak form of the collision integral not only tractable but also very efficient. The variance reduction, achieved by evaluating only the deviation from equilibrium, results in very low statistical uncertainty and the ability to capture arbitrarily small deviations from equilibrium (e.g. low‐flow speed) at a computational cost that is independent of the magnitude of this deviation. As a result, for low‐signal flows the proposed method holds a significant computational advantage compared with traditional particle methods such as direct simulation Monte Carlo (DSMC). Copyright © 2008 John Wiley & Sons, Ltd.     

The evolution equation of joint Pdf of turbulent velocity and dissipation

According to the hypothesis that the dissipation of turbulent kinetic energy satisfies log-normal distribution, a stochastic model of dissipation is provided and the Langevin model^[6] of velocity is modified. Then a joint Pdf equation of turbulent velocity and dissipation is derived. We solve numerically the joint Pdf equation using Monte Carlo method and obtain satisfactory results for decaying turbulence and homogeneous turbulent shear flow. The preliminary results show that the model is well working.