On a Numerical Algorithm for the Modeling of Processes in the Development of a Holographic Relief Image

We construct an algorithm for solving the problem of relief dynamics on the surface of a Newtonian fluid. The risk function is determined by the upper-relaxation method. The velocity field is found by using a two-step difference algorithm that allows one to simplify the calculations and increase the dimension of the system of finite-difference equations. A theorem on stability of the algorithm with respect to the initial data and on convergence of the numerical solution to an exact solution is proved.     

非Newton流体的物质点法模拟研究

准确模拟非Newton流体的运动特性具有重要的工程意义.物质点法作为一种相对新兴的粒子型算法,其结合了Lagrange算法和Euler算法的双重优势,已广泛有效地应用于各个工程领域.基于物质点法,结合人工状态方程,分析了两种非Newton流体(cross流体和幂律流体)在平板Poiseuille流和Couette流情况下的流动特性.结果表明:对Newton流体,物质点模拟结果与理论值一致;对非Newton流体,物质点法可准确模拟其剪切稀化和剪切稠化现象.表明了物质点法在模拟非Newton流体流动问题时的适用性,拓展了物质点法的应用范围.     

Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field

The boundary layer flow of a second grade fluid over a permeable stretching surface with arbitrary velocity and appropriate wall transpiration is investigated. The fluid is electrically conducting in the presence of a constant applied magnetic field. An exact solution to the nonlinear flow problem is presented.     

On a decoupled algorithm for solving a finite element problem for the approximation of viscoelastic fluid flow

Summary. The aim of this work is to study a decoupled algorithm of a fixed point for solving a finite element (FE) problem for the approximation of viscoelastic fluid flow obeying an Oldroyd B differential model. The interest for this algorithm lies in its applications to numerical simulation and in the cost of computing. Furthermore it is easy to bring this algorithm into play. The unknowns are the viscoelastic part of the extra stress tensor, the velocity and the pressure. We suppose that the solution is sufficiently smooth and small. The approximation of stress, velocity and pressure are resp. discontinuous, continuous, continuous FE. Upwinding needed for convection of , is made by discontinuous FE. The method consists to solve alternatively a transport equation for the stress, and a Stokes like problem for velocity and pressure. Previously, results of existence of the solution for the approximate problem and error bounds have been obtained using fixed point techniques with coupled algorithm. In this paper we show that the mapping of the decoupled fixed point algorithm is locally (in a neighbourhood of ) contracting and we obtain existence, unicity (locally) of the solution of the approximate problem and error bounds. Received July 29, 1994 / Revised version received March 13, 1995     

Perturbed integral equation method on determining unknown geometry in fluid flow

We consider an inverse problem arising in fluid flow. An algorithm to find the shape of a body in uniform flow is proposed when the tangential velocity on its boundary is given a priori. The fluid flow is assumed to be inviscid, incompressible and irrotational.The essential idea to develop our algorithm is the boundary modification process toward the solution shape with the help of the perturbed integral equations. The perturbed integral equations are derived from the boundary perturbation. We also give examples exhibiting the reliability for our proposed algorithm.     

An improved model for noise barriers in a moving fluid

We study a problem of diffraction of a cylindrical acoustic wave from an absorbing half plane in a moving fluid introducing Myers' condition [M.K. Myers, On the acoustic boundary condition in the presence of flow, J. Sound Vibration 71 (1980) 429] and present an improved form of the analytic solution for the diffracted field. The importance of the work lies in the fact that Myers' condition (a generalization of Ingard's impedance condition) is now the accepted form of the boundary condition for impedance barriers with flow and hence yields a correct form of the field. The method of solution consists of Fourier transform, Wiener-Hopf technique and the modified method of stationary phase.     

Analytic solution for MHD flow of a third order fluid in a porous channel

The present study investigates the channel flow of a third order fluid. The fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel. Expression for velocity is developed by an analytic method, namely the homotopy analysis method (HAM). Convergence of the obtained solution is properly checked. The feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs. It is observed that unlike the flow of second grade fluid, the obtained solution for a third order fluid is non-similar. Also, the behavior of Hartmann number on the velocity is different to that of the Reynold's number.     

Couette flow of a third-grade fluid with variable magnetic field

This investigation deals with the analytic solution for the time-dependent flow of an incompressible third-grade fluid which is under the influence of a magnetic field of variable strength. The fluid is in an annular region between two coaxial cylinders. The motion is induced due to an inner cylinder with arbitrary velocity. Group theoretic methods are employed to analyse the nonlinear problem and a solution for the velocity field is obtained analytically.     

MHD flow of a Newtonian fluid over a stretching sheet: an approximate solution

An approximate solution to the problem of steady laminar flow of a viscous incompressible electrically conducting fluid over a stretching sheet is presented. The approach is based on the idea of stretching the variables of the flow problem and then using least squares method to minimize the residual of a differential equation. The effects of the magnetic field on the flow characteristics are demonstrated through numerical computations with different values of the Hartman number.     

Self-similar solutions of the magnetohydrodynamic boundary layer system for a non-dilatable fluid

A rigorous mathematical analysis is given for a magnetohydrodynamic boundary layer problem, which arises in the study of self-similar solutions of the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting non-dilatable fluid (i.e., a Newtonian fluid or a pseudo-plastic one) along an isolated surface in the presence of an exterior magnetic field orthogonal to the flow. For this problem, only a normal solution has the physical meaning. The uniqueness, existence, and nonexistence results for normal solutions are established. Also the asymptotic behavior of the normal solution at the infinity is displayed. Received: January 10, 2007; revised: September 6, 2007, April 21, 2008     

广义二阶流体管内轴向流动

在流体的本构关系中引入分数阶导数运算，对于介于粘性与弹性之间的流体的描述更具有合理性。本文将这种关系引入二阶流体，研究其管内轴向流动。我们先求出了１／２阶导数的解析解，用以验证Ｌａｐｌａｃｅ数值反演的ＣＲＵＭＰ方法的有效性。然后用ＣＲＵＭＰ法分析二阶流体管内轴向流动的特征。分析表明粘弹性特征越明显的流体，其速度与应力对分数导数的阶数越具有敏感性。     

Algebraic multilevel method AMG: Comparison with the method BICGSTAB + ILU and its use in the method CPR

The algebraic multilevel method AMG is compared with the method BICGSTAB+ILU on a model problem with a strong anisotropy. The method AMG was used as a part of the method CPR for solution of the filtration problems of a viscous compressible fluid flow in porous media. The algorithm CPR+AMG is compared with CPR+ILU on the base of this problem. The work of the CPR+AMG is analyzed by solving the problem for a model oil field.     

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.     

Analysis and finite element approximation of an optimal control problem for the Oseen viscoelastic fluid flow

In this article we study a boundary control problem for an Oseen-type model of viscoelastic fluid flow. The existence of a unique optimal solution is proved and an optimality system is derived by the first-order necessary condition. We investigate finite element approximations to a solution of the optimality system, and a solution algorithm for the system based on the gradient method.     

Generalized approximation method and a thin film flow of a third grade fluid on a moving belt

We develop a generalized approximation method (GAM) to obtain a solution of a thin film flow of a third grade fluid on a moving belt. The GAM generates a monotone sequence of solutions of linear problems. The sequence of solutions of linear problems converges monotonically and rapidly to a solution of the original nonlinear problem. We present some numerical simulations to illustrate and confirm our results.     

Unsteady hydromagnetic rotating flow of a conducting second grade fluid

The purpose of this work is to investigate the hydromagnetic oscillatory flow of a fluid bounded by a porous plate, when the entire system rotates about an axis normal to the plate. The fluid is assumed to be non-Newtonian (second grade), incompressible and electrically conducting. The magnetic field is applied transversely to the direction of the flow. Such a flow model has great significance not only of its theoretical interest, but also for applications to geophysics and engineering. The resulting initial value problem has been solved analytically for steady and unsteady cases. The analysis of the obtained results showed that the flow field is appreciably influenced by the material parameter of the second grade fluid, the applied magnetic field, the imposed frequency, rotation and suction and blowing parameters. It is observed in a second grade fluid that a steady asymptotic hydromagnetic solution exists for blowing and resonance which is different from the hydrodynamic situation.     

Incipient separation over wall irregularities in transonic flow

Incipient separation over wall irregularities in a steady two dimensional flow field of a perfect fluid which has transonic speed characteristics has been investigated considering viscous-inviscid interactions at high Reynolds number. The aim of this work is to investigate dependence of the critical hump height (when a well attached flow over rigid body surface turns into a separated one) on the Karman–Guderley parameter which characterizes of the local flow field. The analysis of the flow field starts with the so-called inspection analysis of the flow properties and then the interaction problem has been constructed using the asymptotic analysis of triple-deck structure of interaction region. Finally, a method based on a semi-direct solution of governing equations of the transonic interaction problem has been used to obtain the numerical solution of the problem.     

Convergence proof of the velocity field for a stokes flow immersed boundary method

The immersed boundary (IB) method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It is characterized by the use of a uniform Cartesian mesh for the fluid, a Lagrangian curvilinear mesh on the elastic material, and discrete delta functions for communication between the two grids. We consider a simple IB problem in a two‐dimensional periodic fluid domain with a one‐dimensional force generator. We obtain error estimates for the velocity field of the IB solution for the stationary Stokes problem. We use this result to prove convergence of a simple small‐amplitude dynamic problem. We test our error estimates against computational experiments. © 2007 Wiley Periodicals, Inc.     

Solvability of a supercritical free surface flow problem under gravity-capillarity

In this paper, we consider a problem of a supercritical free surface flow over an obstacle lying on the bottom of a channel in 2D. The flow is irrotational, stationary and the fluid is ideal and incompressible. We take into account both the gravity and the effects of the superficial tension. The problem is nonlinear, it is formulated by the Laplace operator and the dynamic condition defined on the free surface of the fluid domain (Bernoulli equation). Using the perturbation stream function, we linearize the problem and we give a priori properties of the solution. These a priori properties allow us to construct a space where we can use the Lax–Milgram’s theorem to prove the existence and the uniqueness of the solution of the problem.     

Existence of a Nonstationary Poiseuille Solution

The nonstationary Poiseuille solution describing the flow of a viscous incompressible fluid in an infinite cylinder is defined as a solution of the inverse problem for the heat equation. The existence and uniqueness of such nonstationary Poiseuille solution with the prescribed flux F(t) of the velocity field is studied. It is proved that under some compatibility conditions on the initial data and flux F(t) the corresponding inverse problem has a unique solution in Holder spaces.Original Russian Text Copyright © 2005 Pileckas K. and Keblikas V.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 649–662, May–June, 2005.