SIMULATION OF THE TWO PHASE FLOW OF DROPLET IMPINGEMENT ON LIQUID FILM BY THE LATTICE BOLTZMANN METHOD

A Lattice Boltzmann Method (LBM) with two-distribution functions is employed for simulating the two-phase flow induced by a liquid droplet impinging onto the film of the same liquid on solid surface.The model is suitable for solution of twophase flow problem at high density and viscosity ratios of liquid to vapor and phase transition between liquid and its vapor.The roles of the vapor flow,the density ratio of liquid to vapor and the surface tension of the droplet in the splashing formation are discussed.It is concluded that the vapour flow induced by the droplet fall and splash in the whole impinging process may affect remarkably the splash behaviour.For the case of large density ratio of liquid to vapor a crown may engender after the droplet collides with the film.However,for the case of small density ratio of liquid to vapor a "bell" like splash may be observed.     

Comparative Statics for the Consumer Problem

This paper studies comparative statics in the consumer utlity maximization problem with two goods. The analysis can be global, and it allows for indivisibilities, discrete changes, and non-binding budget constraints. It does not rely either on topological or convexity assumptions. Instead, it uses lattice programming techniques. The conditions derived are superextremal variant properties on the utility function, in appropriately constructed lattices on the consumption set. Sufficient conditions are given for one or both goods to be normal, for one to be inferior, and for some cases of price effects, using what are called value orders and lattices.     

基于格子玻尔兹曼法的三维溃坝流数值模拟与验证

溃坝问题一直是验证数值模拟方法有效性的经典问题。利用基于格子玻尔兹曼离散方法研发的XFlow软件来模拟三维溃坝问题,以此验证其有效性并提出进一步的改进方向。为了对比前人所做的实验和模拟结果,计算了无障碍三维溃坝流相应监测点的压力、水位等要素,得到了水流演进过程,并提出了用增强固壁函数法处理固壁边界以增强计算的稳定性,另外还考虑了有矩形障碍物的三维溃坝问题。研究结果表明：该方法能捕捉到某一时间点的自由液面,相关数据计算结果准确,且无需划分网格,能减少工作量,但结果稳定性较差,合理运用边界处理方法能有效解决这一问题。     

格子Boltzmann方法在模拟液滴冲击液面中的应用

应用格子Boltzmann两相流方程,结合水平集界面重构技术,提出两相流的数值模型。采用五阶WENO格式和三阶TVD Runge-Kutta格式来求解水平集函数的输运方程。在不计重力的条件下,对液滴平动进行了数值模拟,在计算了800个时间步后,平动的液滴仍然保持原来的形状。在考虑重力的条件下,对液滴在空气中自由下落、液滴冲击液面的全过程进行了数值模拟,精细地刻画了液滴和液面界面的变化过程。数值模拟结果与物理现象一致。     

NUMERICAL STUDY OF THE RELATIONSHIP BETWEEN APPARENT SLIP LENGTH AND CONTACT ANGLE BY LATTICE BOLTZMANN METHOD

The apparent slip between solid wall and liquid is studied by using the Lattice Boltzmann Method (LBM) and theShan-Chen multiphase model in this paper. With a no-slip bounce-back scheme applied to the interface, flow regimes under differentwall wettabilities are investigated. Because of the wall wettability, liquid apparent slip is observed. Slip lengths for different wallwettabilities are found to collapse nearly onto a single curve as a function of the static contact angle, and thereby a relationshipbetween apparent slip length and contact angle is suggested. Our results also show that the wall wettability leads to the formation of alow-density layer between solid wall and liquid, which produced apparent slip in the micro-scale.     

Lattice Boltzmann simulation of solute transport in a single rough fracture

In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.     

LATTICE BOLTZMANN SIMULATIONS OF TRIAGULAR CAVITY FLOW AND FREE-SURFACE PROBLEMS

The Lattice Boltzmann Method (LBM) was investigated to solve triangular cavity flow and free-surface problems in hydraulic dynamics. Some cases of triangular cavity flow and backward step flow were simulated to show the efficiency and stability of this method. Two-dimensional partial dam breaking problem and the propagation and diffraction of dam-break wave around rectangular and circular cylinder were numerically studied successfully. Excellent agreement was obtained between numerical predictions and available results.     

振荡层流边界层运动的格子Boltzmann模拟

将波浪作用下的振荡边界层问题化为振动平板边界层问题，利用格子Boltzmann方法中不可压缩的模型模拟了线性波和椭圆余弦波作用下的层流边界层流速变化，并和理论解进行了比较。算例表明，不同波浪条件下的数值模拟结果和理论解吻合较好，仅在流速较小的相位时两者在近床面处有较大误差，误差的形成主要与边界条件的精度有关。     

基于闭包系统划分的概念格并行构造算法

随着处理的形式背景的增大，概念格的时空复杂度也会随着急剧增大。研究新的方法和手段来构造概念格，是概念格技术应用于大型复杂数据系统的前提．提高其构造效率的一种有效途径是利用高性能并行计算机和网络并行计算的能力，因此概念格的并行构造算法已成为众多学者的一个新的研究方向。概念格的并行构造思想就是根据不同的原理，采用分治策略，通过对形式背景的拆分，形成分布存储的多个子背景，然后构造相应的子概念格，再由子概念格的合并得到所需的概念格。目前建格算法的分布处理研究主要有形式背景的并置和叠置以及形式背景的折叠搜索子空间划分两种方法，本文在总结研究这两种方法的基础上，基于偏序集上闭包系统分解的思想，对提出的闭包系统划分为多个子闭包系统的判定定理进行了证明．使闭包系统的分解既不会产生冗余信息，也不会使信息丢失，并把所提出的判定定理用于概念格的并行处理．提出了一个新的基于闭包划分的概念格并行生成算法——Para-Prumng算法。通过实验，利用随机生成的数据集同经典NextClosure算法进行比较分析，验证了新算法的正确性和有效性。     

A nonsmooth approach to envelope theorems

We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian–Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.