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2002 | Buch | 3. Auflage

Basic Concepts of Fluid Flow Kapitel lesen Erstes Kapitel lesen

Computational Methods for Fluid Dynamics

verfasst von: Professor Joel H. Ferziger, Dr. Milovan Perić

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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Über dieses Buch

In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.

Inhaltsverzeichnis

Frontmatter
1. Basic Concepts of Fluid Flow
Abstract
Fluids are substances whose molecular structure offers no resistance to external shear forces: even the smallest force causes deformation of a fluid particle. Although a significant distinction exists between liquids and gases, both types of fluids obey the same laws of motion. In most cases of interest, a fluid can be regarded as continuum, i.e, a continuous substance.
Joel H. Ferziger, Milovan Perić
2. Introduction to Numerical Methods
Abstract
As the first chapter stated, the equations of fluid mechanics — which have been known for over a century — are solvable for only a limited number of flows. The known solutions are extremely useful in helping to underst and fluid flow but rarely can they be used directly in engineering analysis or design. The engineer has traditionally been forced to use other approaches.
Joel H. Ferziger, Milovan Perić
3. Finite Difference Methods
Abstract
As was mentioned in Chap. 1, all conservation equations have similar structure and may be regarded as special cases of a generic transport equation, Eq. (1.26), (1.27) or (1.28). For this reason, we shall treat only a single, generic conservation equation in this and the following chapters. It will be used to demonstrate discretization methods for the terms which are common to all conservation equations (convection, diffusion, and sources). The special features of the Navier-Stokes equations and techniques for solving coupled non-linear problems will be introduced later. Also, for the time being, the unsteady term will be dropped so we consider only time-independent problems.
Joel H. Ferziger, Milovan Perić
4. Finite Volume Methods
Abstract
As in the previous chapter, we consider only the generic conservation equation for a quantity ϕ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point:
$$ \int_s {\rho \varphi v \cdot ndS = } \int_s {\Gamma grad\varphi \cdot ndS + \int_\Omega q } _\varphi d\Omega $$
(4.1)
The solution domain is subdivided into a finite number of small control volumes (CVs) by a grid which, in contrast to the finite difference (FD) method, defines the control volume boundaries, not the computational nodes. For the sake of simplicity we shall demonstrate the method using Cartesian grids; complex geometries are treated in Chap. 8.M
Joel H. Ferziger, Milovan Perić
5. Solution of Linear Equation System
Abstract
In the previous two chapters we showed how the convection-diffusion equation may be discretized using FD and FV methods. In either case, the result of the discretization process is a system of algebraic equations, which are linear or non-linear according to the nature of the partial differential equation(s) from which they are derived. In the non-linear case, the discretized equations must be solved by an iterative technique that involves guessing a solution, linearizing the equations about that solution, and improving the solution; the process is repeated until a converged result is obtained. So, whether the equations are linear or not, efficient methods for solving linear systems of algebraic equations are needed.
Joel H. Ferziger, Milovan Perić
6. Methods for Unsteady Problems
Abstract
In computing unsteady flows, we have a fourth coordinate direction to consider: time. Just as with the space coordinates, time must be discretized. We can consider the time “grid” in either the finite difference spirit , as discrete points in time, or in a finite volume view as “time volumes” . The major difference between the space and time coordinates lies in the direct ion of influence: whereas a force at any space location may (in elliptic problems) influence the flow anywhere else, forcing at a given instant will affect the flow only in the future - there is no backward influence. Unsteady flows are, therefore, parabolic-like in time. This means that no conditions can be imposed on the solution (except at the boundaries) at any time after the initiation of the calculation, which has a strong influence on the choice of solution strategy. To be faithful to the nature of time, essentially all solution methods advance in time in a step-by-step or “marching” manner. These methods are very similar to ones applied to initial value problems for ordinary differential equations (ODEs) so we shall give a brief review of such methods in t he next section.
Joel H. Ferziger, Milovan Perić
7. Solution of the Navier-Stokes Equations
Abstract
In Chaps. 3, 4 and 6 we dealt with the discretization of a generic conservation equation. The discretization principles described there apply to the momentum and continuity equations (which we shall collectively call the Navier-Stokes equations) . In this chapter, we shall describe how the terms in the momentum equations which differ from those in the generic conservation equation are treated.
Joel H. Ferziger, Milovan Perić
8. Complex Geometries
Abstract
Most flows in engineering practice involve complex geometries which are not readily fit with Cartesian grids. Although the principles of discretization and solution methods for algebraic systems described earlier may be used, many modifications are required. The properties of the solution algorithm depend on the choices of the grid and of the vector and tensor components, and the arrangement of variables on the grid. These issues are discussed in this chapter.
Joel H. Ferziger, Milovan Perić
9. Turbulent Flows
Abstract
Most flows encountered in engineering practice are turbulent and therefore require different treatment. Turbulent flows are characterized by the following properties:
  • Turbulent flows are highly unsteady. A plot of the velocity as a function of time at most points in the flow would appear random to an observer unfamiliar with these flows. The word ‘chaotic’ could be used but it has been given another definition in recent years.
  • They are three-dimensional. The time-averaged velocity may be a function of only two coordinates, but the instantaneous field fluctuates rapidly in all three spatial dimensions.
  • They contain a great deal of vorticity. Indeed, vortex stretching is one of the principal mechanisms by which the intensity of turbulence is increased.
  • Turbulence increases the rate at which conserved quantities are stirred. Stirring is a process in which parcels of fluid with differing concentrations of at least one of the conserved properties are brought into contact. The actual mixing is accomplished by diffusion. Nonetheless, this process is often called turbulent diffusion.
  • By means of the processes just mentioned, turbulence brings fluids of differing momentum content into contact. The reduction of the velocity gradients due to the action of viscosity reduces the kinetic energy of the flow; in other words, mixing is a dissipative process. The lost energy is irreversibly converted into internal energy of the fluid.
  • It has been shown in recent years that turbulent flows contain coherent structures-repeatable and essentially deterministic events that are responsible for a large part of the mixing. However, the random component of turbulent flows causes these events to differ from each other in size, strength, and time interval between occurrences, making study of them very difficult.
  • Turbulent flows fluctuate on a broad range of length and time scales. This property makes direct numerical simulation of turbulent flows very difficult. (See below.)
Joel H. Ferziger, Milovan Perić
10. Compressible Flow
Abstract
Compressible flows are important in aerodynamics and turbomachinery among other applications. In high speed flows around aircraft, the Reynolds numbers are extremely high and turbulence effects are confined to thin boundary layers. The drag consists of two components, frictional drag due to the boundary layer and pressure or form drag which is essentially inviscid in nature; there may also be wave drag due to shocks which may be computed from the inviscid equations provided that care is taken to assure that the second law of thermodynamics is obeyed. If frictional drag is ignored, these flows may be computed using the inviscid momentum Euler equations.
Joel H. Ferziger, Milovan Perić
11. Efficiency and Accuracy Improvement
Abstract
The best measure of the efficiency of a solution method is the computational effort required to achieve the desired accuracy. There are several methods for improving the efficiency and accuracy of CFD methods; we shall present three that are general enough to be applied to any of t he solution schemes described in previous chapters.
Joel H. Ferziger, Milovan Perić
12. Special Topics
Abstract
Fluid flows may include a broad range of additional physical phenomena that take the subject far beyond the single-phase non-reacting flows that have been the focus of this work up to this point. Many types of physical processes may occur in flowing fluids. Each of these may interact with the flow to produce an amazing range of new phenomena. Almost all of these processes occur in important applications. Computational methods have been applied to them with varying degrees of success.
Joel H. Ferziger, Milovan Perić
Backmatter
Metadaten
Titel
Computational Methods for Fluid Dynamics
verfasst von
Professor Joel H. Ferziger
Dr. Milovan Perić
Copyright-Jahr
2002
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-56026-2
Print ISBN
978-3-540-42074-3
DOI
https://doi.org/10.1007/978-3-642-56026-2