Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality.     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid

Fully developed laminar mixed convection of a nanofluid consists of water and Al₂O₃ in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al₂O₃. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°.     

U型管内液柱振动的演示实验研究

根据实验结果，分析了影响U型管中液柱振动的各种因素，给出了获得好的演示效果的改进措施．     

Banach空间非线性混合型微分-积分方程整体解的存在性和唯一解

研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.     

Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.