Computation of dilute two-phase flow in a pump

This paper is a report on a joint project between academia and industry which is concerned with computation of dilute two-phase flow through a pump in turbulent condition. The flow field for the continuous phase is computed using the Reynolds averaged Navier–Stokes equations together with mixing length turbulence modeling. The dispersed phase is treated using the Lagrangian approach by tracking it's trajectory along which the information is passed. It is found that the bubbles and small solid particles flow out of the chamber (between the rotating impeller and the casing wall) with the conveying fluid. The solid particles of relatively bigger sizes accumulate at the low pressure zones near the cashing wall or the rotating shaft.     

求解二次分配问题的拉格朗日松弛新方法

以改进的拉格朗日松弛(Lagrangian relaxation,LR)方法和二次分配问题(quadratic assignment problem,QAP)的线性化模型为基础,给出了求解QAP的拉格朗日松弛新方法,这为有效求解QAP提供了一种新的解决方案.通过求解二次分配基准问题库(QAPLIB)中的实际算例,从实验的角度说明了拉格朗日松弛新方法求解QAP的可行性及存在的不足之处,并对今后进一步的研究工作指明了方向.     

运输问题的改进算法探讨

探讨了运输问题表上作业法初始解的取得和最优解的判断，在一定程度上可以省略表上作业法的方案调整过程，从而简便了求解运输问题的最优解的过程。     

On the Equivalence of the Simplex Methods and a Multiplier-Alike Method for Linear Programming

In linear programming, the simplex method has been viewed for a long time as an efficient tool. Interior methods have attracted a lot of attention since they were proposed recently. It seems plausible intuitively that there is no reason why a good linear programming algorithm should not be allowed to cross the boundary of the feasible region when necessary. However, such an algorithm is seldom studied. In this paper, we will develop first a framework of a multiplier-alike algorithm for linear programming which allows its trajectory to move across the boundary of the feasible region. Second, we illustrate that such a framework has the potential to perform as well as the simplex method by showing that these methods are equivalent in a well-defined sense, even though they look so different.     

Semigroup Properties and the Crandall Liggett Approximation for a Class of Differential Equations with State-Dependent Delays

We present an approach for the resolution of a class of differential equations with state-dependent delays by the theory of strongly continuous nonlinear semigroups. We show that this class determines a strongly continuous semigroup in a closed subset of C^0, 1. We characterize the infinitesimal generator of this semigroup through its domain. Finally, an approximation of the Crandall-Liggett type for the semigroup is obtained in a dense subset of (C, ‖·‖_∞). As far as we know this approach is new in the context of state-dependent delay equations while it is classical in the case of constant delay differential equations.     

An Improved Linearity-Preserving Cell-Centered Scheme for Nonlinear Diffusion Problems on General Meshes

In this paper, we suggest a new vertex interpolation algorithm to improve an existing cell-centered finite volume scheme for nonlinear diffusion problems on general meshes. The new vertex interpolation algorithm is derived by applying a special limit procedure to the well-known MPFA-O method. Since the MPFA-O method for 3D cases has been addressed in some studies, the new vertex interpolation algorithm can be extended to 3D cases naturally. More interesting is that the solvability of the corresponding local system is proved under some assumptions. Additionally, we modify the edge flux approximation by an edge-based discretization of diffusion coefficient, and thus the improved scheme is free of the so-called numerical heat-barrier issue suffered by many existing cell-centered or hybrid schemes. The final scheme allows arbitrary continuous or discontinuous diffusion coefficients and can be applicable to arbitrary star-shaped polygonal meshes. A second-order convergence rate for the approximate solution and a first-order accuracy for the flux are observed in numerical experiments. In the comparative experiments with some existing vertex interpolation algorithms, the new algorithm shows obvious improvement on highly distorted meshes.     

A new conservation theorem

A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Bäcklund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.     

求不定二次规划全局解的一个新算法

本文提出了一个求不定二次规划问题全局最优解的新算法.首先,给出了三种计算下界的方法:线性逼近法、凸松弛法和拉格朗日松弛法;并且证明了拉格朗日对偶界与通过凸松弛得到的下界是相等的;然后建立了基于拉格朗日对偶界和矩形两分法的分枝定界算法,并给出了初步的数值试验结果.     

Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps

In the framework of locally convex topological vector spaces, we establish a scalarization theorem, a Lagrange multiplier theorem and duality theorems for superefficiency in vector optimization involving nearly subconvexlike set-valued maps.     

A location-routing problem for the conversion to the “click-and-mortar” retailing: The static case

The static conversion from brick-and-mortar retailing to the hybrid click-and-mortar business model is studied from the perspective of distribution logistics. Retailers run warehouses and brick-and-mortar stores to meet the demand of their walk-in customers. When they decide to operate on the Web as an e-tailer, also click-and-mortar stores are needed which can serve both walk-in and online customers. While the distance between home and the nearest open store is used as a proxy measure for walk-in customers, a quality of service (QoS) guarantee for online customers is timely delivery of their orders. We describe and solve a static location-routing based problem for companies that embrace the clicks-and-bricks strategy in their retail operations. An augmented Lagrangian relaxation method embedded in a subgradient optimization procedure generates lower bounds, whereas a heuristic method finds feasible solutions. The performance of the Lagrangian-based solution method is tested on a number of randomly generated test problems.