Brachistochrone with Coulomb friction as the solution of an isoperimetrical variational problem

The problem of finding the plane supporting curve (brachistochrone) along which a heavy particle released from rest at the given starting point slides with dry (Coulomb) friction and reaches the given destination point in least time, is stated as a variational isoperimetrical problem. The finite parametric equations of the extremal curve are obtained. This curve is the sought-for brachistochrone if the solution of the problem exists. Several numerical examples are given.     

MHD free convective flow past semi-infinite vertical permeable wall

In this paper,the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partia...     

A boundary condition for arbitrary shaped inlets in lattice–Boltzmann simulations

We introduce a mass‐flux‐based inlet boundary condition for the lattice‐Boltzmann method. The proposed boundary condition requires minimal amount of boundary data, it produces a steady‐state velocity field which is accurate close to the inlet even for arbitrary inlet geometries, and yet it is simple to implement. We demonstrate its capability for both simple and complex inlet geometries by numerical experiments. For simple inlet geometries, we show that the boundary condition provides very accurate inlet velocities when Re?1. Even with moderate Reynolds number, the inlet velocities are accurate for practical purposes. Furthermore, the potential of our boundary condition to produce inlet velocities which convincingly adapt to complex inlet geometries is highlighted with two specific examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Internal flow numerical simulation of a cross‐flow fan in refrigerant operating condition using user‐defined functions

In the paper, a cross‐flow fan in refrigerant operating condition is systematically simulated using user‐defined functions. Three‐dimensional simulations are acquired with Navier–Stokes equations coupled with k–ε turbulence model, and internal flow characteristics of an indoor split‐type air conditioner are obtained, which is mainly composed of cross‐flow fan and heat exchanger. It has systematically been simulated in the isothermal flow condition that the performance of cross‐flow fan may be reduced easily with dry or humid air, and in the refrigerant operating condition in which user‐defined functions are applied to the humid air, considered as a mixture of dry air and vapor. A density‐modulated function is adopted to deal with the condensation of the vapor at the heat‐transfer region approximately. The results show flow mechanism of the two gas‐phase flow, including phase‐vary process. The distribution of the parameters is not uniform at the inlet of the machine, the intensity and position of pressure and velocity vary along the axial direction of the fan, the distribution of vapor volume fraction and turbulent intensity in heat‐transfer region is obtained, and the external characteristic data of the indoor machine are obtained and analyzed. Compared with the experimental data, the calculated characteristic curves and designed parameters are on target. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.     

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes–Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.     

A Free Boundary Problem for an Elliptic–Parabolic System: Application to a Model of Tumor Growth

Abstract

In this article, we study a free boundary problem for a system of two partial differential equations, one parabolic and other elliptic. The system models the growth of a tumor with arbitrary initial shape. We establish the existence and uniqueness of a solution for some time interval. In the special case where we only have the elliptic equation, the problem coincides with the Hele–Shaw problem.     

Existence and Non-Existence Results for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions

Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition between the different growths of the nonlinearities.     

A Class of Operator Equations in Nonlinear Mechanics

A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.”

AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15.     

Comparison of non‐reflective boundary conditions for a free‐rising turbulent axisymmetric plume

The stability and accuracy of radiation type non‐reflective outflow boundary conditions, as well as the standard Neumann boundary condition with zero normal derivative, have been compared for the numerical simulation of a turbulent axisymmetric plume with Reynolds number of 7700 and Prandtl number of 0.71. Comparison of the performance of the boundary conditions with respect to each other, and to the results obtained for an extended domain, shows that a one‐dimensional scheme in which advection and diffusion terms are included in the radiation equation is the optimum approach for the plume simulation. Copyright © 2013 John Wiley & Sons, Ltd.     

Formulation of commons dilemma: Dawes model reconsidered

This paper examines Dawes (1975) model on commons dilemma (CD) situation and proposes an alternative model which formulates CD. Firstly, it makes clear that Dawes model does not have the characteristics of CD. Secondly, it specifies “resource unit condition” which models of commons dilemma must satisfy. Thirdly, it presents CD model, which is obtained by setting the condition in Dawes model. And lastly, it examines some nature of the proposed model and find that in CD situation, fine is distributed proportionally to each player's property.