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The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre­ hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa­ chusetts Institute of Technology researchers. Chapter 3 describes the gen­ eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.

Inhaltsverzeichnis

Frontmatter

Chapter 1. A Brief Review of Previous Work on Viscous Flow Simulation

Abstract
The numerical analysis of fluid mechanics and heat transfer has become recognized as a new research field called “Computational Fluid Dynamics” or “Numerical Fluid Mechanics” [1, 2]. Their emergence has been detected by the rapid development of computers and the difficulty of using the experimental approach.
K. Kitagawa

Chapter 2. Boundary Element Formulation for Viscous Compressible Flow

Abstract
Three main methods of solution are presently being applied in general Navier Stokes solvers. They are: (i) Finite Differences, (ii) Finite Elements (iii) Finite Volume
C. A. Brebbia, J. J. Connor

Chapter 3. A Generalized Formulation for Unsteady Viscous Flow Problems

Abstract
With the increased availability of high speed computers and improved numerical algorithms, it is now possible to solve numerically many steady and unsteady viscous flows past arbitrary airfoils. A survey of literature shows that investigators in the past have taken one of the following two avenues:
a)
weak viscous-inviscid interaction and its extension to separated flows,
 
b)
numerical solution of the Navier-Stokes equations over the entire computational domain.
 
J. C. Wu, U. Gulcat, C. M. Wang, N. L. Sankar

Chapter 4. Natural and Forced Convection Simulation Using the Velocity-Vorticity Approach

Abstract
The partial differential equations set, governing the laminar motion of viscous incompressible fluid is known as nonlinear Navier-Stokes equation. They constitute the statement of the basic conservation ballance of mass, momentum, and energy, applied to a control volume, i.e. the Eulerian description. This equation system is generally considered to be the fundamental description for all laminar as well as for turbulent flows, although some statistical averaging procedure is needed (e.g. Reynolds equations for turbulence) to simulate numerically the flow at high Re number values due to the enormous computational effort required.
P. Skerget, A. Alujevic, C. A. Brebbia, G. Kuhn

Chapter 5. A Boundary Element Analysis for Thermal Convection Problems

Abstract
In recent years, the rapid development of computers has been utilized for applying numerical analyses to solve a variety of problems in the scientific and engineering fields. Especially, the numerical analysis of fluid flow problems has become recognized as a new subject called Numerical fluid mechanics or Computational fluid mechanics.
K. Kitagawa, C. A. Brebbia, M. Tanaka

Chapter 6. Calculation of the Potential Flow with Consideration of the Boundary Layer

Abstract
The three-dimensional steady laminar flow of a viscous incompressible fluid around an arbitrary body shall be treated. This can be done by solving the Navier-Stokes equation using a finite difference method. If the Reynolds number is high, this very cumbersome method can be replaced by another one taking account of the fact, that in this case the viscous effects essentially are confined to the boundary layer at the body surface and to free shear layers. Thus the solution of the problem can be composed of that of the inviscid outer flow, i.e. the potential flow, and of the viscous inner flow (see for example Kevorkian and Cole [1]). The first can be calculated by boundary element methods, the second by finite difference methods.
H. Schmitt, G. R. Schneider

Chapter 7. Applications in Non-Newtonian Fluid Mechanics

Abstract
The majority of the fluids dealt with by Engineers and Scientists, such as air, water and oils, can be regarded as Newtonian under most conditions of interest. However, in many cases the assumption of Newtonian behaviour is not valid and the rather more complex non-Newtonian response must be modelled. Such situations arise in the chemical processing industry and plastics processing industry. Non-Newtonian behaviour is also encountered in the mining industry, where slurries and muds are often handled, and in applications such as lubrication and biomedical flows. The simulation of non-Newtonian fluid flow phenomena is therefore of importance to industry.
M. B. Bush

Chapter 8. Viscous Fluid Mechanics

Abstract
First we give the governing equations for an incompressible viscous newtonian fluid completed with boundary conditions.
An integral equation method for two-dimensional Stokes flows is presented which consists in solving the biharmonic equation.
A direct boundary integral formulation is developed for the biharmonic equation. The representation of the stream function and its derivative obtained involves all the quantities defined on the boundary.
In the case of Stokes flow the discretization of these representations leads to a linear system of equations.
When the inertia effects are taken into account, the evaluation of these terms is necessary. In this latter case four internal parameters are defined: the two components of the velocity and the two gradients of the vorticity. By discretizing the domain we obtain nonlinear algebraic equations which can be solved by classical method for small Reynold’s numbers, but much elaborated methods are necessary when the inertia effects are important.
Finally we present some examples which prove the numerical efficiency of this formulation compared with results given by other methods.
D. Bonneau, G. Bezine

Backmatter

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