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2016 | Buch

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Fully Implicit, Coupled Procedures in Computational Fluid Dynamics

An Engineer's Resource Book

verfasst von: Zeka Mazhar

Verlag: Springer International Publishing

Buchreihe : Fluid Mechanics and Its Applications

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book introduces a new generation of superfast algorithms for the treatment of the notoriously difficult velocity-pressure coupling problem in incompressible fluid flow solutions. It provides all the necessary details for the understanding and implementation of the procedures. The derivation and construction of the fully-implicit, block-coupled, incomplete decomposition mechanism are given in a systematic, but easy fashion. Worked-out solutions are included, with comparisons and discussions. A complete program code is included for faster implementation of the algorithm. A brief literature review of the development of the classical solution procedures is included as well.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

This chapter contains an overview of the aims and scope of the book. It describes the need for an easy and efficient way of speeding up the convergence rates of the solution procedures for field problems. It is pointed out that a new view point is necessary in order to break down the stagnant slow convergence and stability problems of the classical segregated or pressure-based algorithms. A short description of the outline of the book is included.

Zeka Mazhar

Chapter 2. Preliminaries

Abstract

This chapter introduces mathematical preliminaries necessary for the discretization of the governing equations and certain techniques for the solution of the special types of resulting linear sub-systems.

Zeka Mazhar

Chapter 3. Governing Differential Equations

Abstract

In this chapter, the set of basic differential equations governing field problems is introduced. This is followed by a review of the special features of these equations and the difficulties involved in their solutions. Special emphasis is given to the crucial velocity-pressure coupling problem by verifying the need for the new viewpoint applied in the proposed procedures.

Zeka Mazhar

Chapter 4. Finite Difference Formulations

Abstract

This chapter is devoted to introduce, in full, the discretization process for the governing equations, utilizing some enhanced versions of the approximations derived in Chap. 2.

Zeka Mazhar

Chapter 5. Preparations for Solution

Abstract

In this chapter, certain preparatory processes which are necessary prior to the actual solution process, are presented in detail. These include the discretization of the solution region and the node numbering convention, simultaneous application of various types of boundary conditions on the momentum and mass conservation equations and relaxation enforcement.

Zeka Mazhar

Chapter 6. Assembling the Discretized Equations into a Block Matrix System

Abstract

In this chapter, the discretized forms of the mass and momentum conservation equations are assembled into a block-coupled system of linear equations. The numbering strategy and the structure of the resulting system are presented. Finally, the difficulties involved in the solution of the resulting system are discussed.

Zeka Mazhar

Chapter 7. The Solution Procedure: Block Incomplete Decomposition

Abstract

This is the main chapter in which the fully implicit clock-coupled solution strategy is introduced. First a discussion on the advantages of the block system are presented, followed by a general incomplete decomposition process. Then, the technique is applied to the block-coupled system and the relevant equations are derived. Based on the new technique, possible alternatives are presented leading to a family of procedures. The storage requirements and complexity of the algorithms are also presented.

Zeka Mazhar

Chapter 8. Applications and Testing

Abstract

In this chapter, the procedures presented in the previous chapters are applied on certain, well established benchmark problems. Convergence, stability and cost comparisons are provided in detail for problems of various sizes. Comparison of one of the selected procedures with a classical segregated one (SIMPLER) is also presented. A discussion on the mechanism of the procedures both numerically and physically is provided to answer the question of why the procedures converge so fast and they are so stable.

Zeka Mazhar

Chapter 9. Special Cases

Abstract

This chapter presents brief discussions on the application of the presented procedures to cases which were not discussed in the previous chapters. The issues discussed include time dependent problems, turbulent flows and heat transfer. Adaptation to 3D problems is also explained in detail.

Zeka Mazhar

Chapter 10. Concluding Remarks

Abstract

In this chapter, a few final comments on the presented procedures are provided together with some suggestions for further enhancements.

Zeka Mazhar

Backmatter

Titel: Fully Implicit, Coupled Procedures in Computational Fluid Dynamics
verfasst von: Zeka Mazhar
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-29895-5
Print ISBN: 978-3-319-29894-8
DOI: https://doi.org/10.1007/978-3-319-29895-5

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