A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

Determination of the rheological behavior of epoxy–amine thermosets by dynamic mechanical analysis: Isothermal methods versus nonisothermal methods

The reticulation process of an epoxy resin using an amine as a cure agent was studied at different temperatures and concentrations of the cure agent with dynamic mechanical thermal analysis. The study was performed under both isothermal and nonisothermal conditions, and a temperature–time–transformation diagram was obtained. The measurements from the two modes gave similar results, although the nonisothermal mode required fewer experiments. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1965–1977, 2003     

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

The dynamics of a two-component fluid in the presence of capillary forces

In the present paper we study the qualitative behavior ast→∞ of the solution of the Cauchy problem for a system of equations describing a dynamics of a two-component viscous fluid. The model under consideration takes into account the mutual diffusion of the fluid components as well as their capillary interaction. We describe the ω-limit set of trajectories of the dynamical system generated by the problem. It is proved that the stationary solution of the problem, is a homogeneous stationary distribution of one of the components, is asymptotically stable. Any other stationary solution is not asymptotically stable and is even unstable if there are no close stationary solutions corresponding to a smaller energy level. Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 293–305, August, 1997. Translated by A. M. Chebotarev     

Bianchi type-V model with a perfect fluid and A-term

A self-consistent system of gravitational field with a binary mixture of perfect fluid and dark energy given by a cosmological constant has been considered in Bianchi Type-V universe. The perfect fluid is chosen to be obeying either the equation of state p=γρ with γ ε |0,1| or a van der Waals equation of state. The role of A-term in the evolution of the Bianchi Type-V universe has been studied.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

存在滑移时两圆球间的幂律流体挤压流动

基于Reynolds润滑理论分析了壁面滑移对任意圆球颗粒间幂律流体的挤压流动的影响。研究表明有壁面滑移时挤压流动的粘性力可通过引进本文定义的滑移修正系数分离出无滑移解。推导出的挤压力滑移修正系数是一积分表达式，依赖于滑移参数、幂律指数、球间隙和积分上限。一般地壁面滑移导致粘性力减小，粘性力的减小量随幂律指数的增大而增大，表明壁面滑移对剪切增稠流变材料有更大的影响；粘性力的减小量还随着滑移参数的增大而增加，而这恰与假设相符合；粘性力的减小量又随球间隙减小或积分上限的增大（从液桥情况到完全浸渍）而减小直到趋于常数，这一特性在离散元模拟时可以有效地减少计算量。     

Ionic nanocomposites based on XNBR-OMg filled with layered nanoclays

Ionic elastomers based on carboxylated nitrile rubber (XNBR) crosslinked with magnesium oxide (OMg) and filled with layered nanoclays have been prepared. Two types of nanofillers were employed: a commercial one (Cloisite 15 A) and the other prepared in our laboratory (BCA-ODA). The properties of raw and vulcanized compounds have been studied in order to elucidate the effect of layered nanoclays. X-ray diffraction analysis shows that during compounding and crosslinking the macromolecular chains of rubber were intercalated in a commercial nanofiller, whilst our nanoclay was exfoliated. However, this fact does not affect the properties of compounds homogeneously. Vulcanization parameters, Mooney viscosity and decay and rheological properties were affected depending on the filler type. Mechanical properties were not significantly varied, but glass transition temperature and ionic transition temperature were shifted in comparison with those of the unfilled compound.     

One case of vortex motion in fluid

This text presents an English translation of the significant paper [6] on vortex dynamics published by the outstanding Russian scientist S. A. Chaplygin, which seems to have almost escaped the attention of later investigators in this field. Although it was published more than a century ago, in our opinion it is still interesting and valuable. __________ Originally published in: Trudy otdeleniya fizicheskikh nauk imperatorskogo Moskovskogo obshchestva lyubitelei estestvoznaniya, antropologii i etnografii (Transactions of the Physical Section of Moscow Society of Friends of Natural Sciences, Anthropology and Ethnography), 1903, Vol. 11, No. 2, pp. 11–14. Translated from Russian by S. Ramodanov; edited by D. Blackmore; commented by V. V. Meleshko (Department of Theoretical and Applied Mechanics, Faculty of Machanics and Mathematics, Kiev National Taras Shevchenko University, 01030 Kiev, Ukraine. E-mail: meleshko@univ.kiev.ua) and G.J.F. van Heijst (Fluid Dynamics Laboratory, Faculty of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands. E-mail: g.j.f.v.heijst@tue.nl).