Description
This book is primarily for a first one-semester course on CFD; in mechanical, chemical, and aeronautical engineering. Almost all the existing books on CFD assume knowledge of mathematics in general and differential calculus as well as numerical methods in particular; thus, limiting the readership mostly to the postgraduate curriculum. In this book, an attempt is made to simplify the subject even for readers who have little or no experience in CFD, and without prior knowledge of fluid-dynamics, heattransfer and numerical-methods. The major emphasis is on simplification of the mathematics involved by presenting physical-law (instead of the traditional differential equations) based algebraic-formulations, discussions, and solution-methodology. The physical law based simplified CFD approach (proposed in this book for the first time) keeps the level of mathematics to school education, and also allows the reader to intuitively get started with the computer-programming. Another distinguishing feature of the present book is to effectively link the theory with the computer-program (code). This is done with more pictorial as well as detailed explanation of the numerical methodology. Furthermore, the present book is structured for a module-by-module code-development of the two-dimensional numerical formulation; the codes are given for 2D heat conduction, advection and convection. The present subject involves learning to develop and effectively use a product - a CFD software. The details for the CFD development presented here is the main part of a CFD software. Furthermore, CFD application and analysis are presented by carefully designed example as well as exercise problems; not only limited to fluid dynamics but also includes heat transfer. The reader is trained for a job as CFD developer as well as CFD application engineer; and can also lead to start-ups on the development of "apps" (customized CFD software) for various engineering applications.
"Atul has championed the finite volume method which is now the industry standard. He knows the conventional method of discretizing differential equations but has never been satisfied with it. As a result, he has developed a principle that physical laws that characterize the differential equations should be reflected at every stage of discretization and every stage of approximation. This new CFD book is comprehensive and has a stamp of originality of the author. It will bring students closer to the subject and enable them to contribute to it."
—Dr. K. Muralidhar, IIT Kanpur, INDIA
Chapter
1.1.2 Analogy with a Video-Camera
1.3 Novelty, Scope, and Purpose of this Book
2. Introduction to CFD: Development, Application, and Analysis
2.1.1 Grid Generation: Pre-Processor
2.1.2 Discretization Method: Algebraic Formulation
2.1.3 Solution Methodology: Solver
2.1.4 Computation of Engineering-Parameters:
Post-Processor
3. Essentials of Fluid-Dynamics and Heat-Transfer for CFD
3.1.1 Fundamental/Conservation Laws
3.2 Momentum and Energy Transport Mechanisms
3.3 Physical Law based Differential Formulation
3.3.1 Continuity Equation
3.4 Generalized Volumetric and Flux Terms, and their Differential Formulation
3.5 Mathematical Formulation
3.5.2 Non-Dimensional Study
4. Essentials of Numerical-Methods for CFD
4.1 Finite Difference Method: A Differential to Algebraic Formulation for Governing PDE and BCs
4.1.2 Finite Difference Method
4.1.3 Applications to CFD
4.2 Iterative Solution of System of LAEs for a Flow Property
4.2.2 Applications to CFD
4.3 Numerical Differentiation for Local Engineering Parameters
4.3.1 Differentiation Formulas
4.3.2 Applications to CFD
4.4 Numerical Integration for the Total value of Engineering-Parameters
4.4.2 Applications to CFD
Part II. CFD FOR A CARTESIAN-GEOMETRY
5. Computational Heat Conduction
5.1 Physical Law based Finite Volume Method
5.1.1 Energy Conservation Law for a Control Volume
5.1.2 Algebraic Formulation
5.1.4 Approximated Algebraic-Formulation
5.2 Finite Difference Method for Boundary Conditions
5.3 Flux based Solution Methodology on a Uniform Grid: Explicit-Method
5.3.1 One-Dimensional Conduction
5.3.2 Two-Dimensional Conduction
5.4 Coefficients of LAEs based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method
5.4.1 One-Dimensional Conduction
5.4.2 Two-Dimensional Conduction
6.
Computational Heat Advection
6.1 Physical Law based Finite Volume Method
6.1.1 Energy Conservation Law for a Control Volume
6.1.2 Algebraic Formulation
6.1.4 Approximated Algebraic Formulation
6.2 Flux based Solution Methodology on a Uniform Grid: Explicit-Method
6.2.2 Implementation Details
6.3 Coefficients of LAEs based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method
6.3.1 Advection Scheme on a Non-Uniform Grid
6.3.2 Explicit and Implicit Method
6.3.3 Implementation Details
7.
Computational Heat Convection
7.1 Physical Law based Finite Volume Method
7.1.1 Energy Conservation Law for a Control Volume
7.1.2 Algebraic Formulation
7.1.3 Approximated Algebraic Formulation
7.2 Flux based Solution Methodology on a Uniform Grid: Explicit-Method
7.2.2 Implementation Details
7.3 Coefficients of LAEs based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method
8.
Computational Fluid Dynamics: Physical Law based Finite Volume Method
8.1 Generalized Variables for the Combined Heat and Fluid Flow
8.2 Conservation Laws for a Control Volume
8.3 Algebraic Formulation
8.5 Approximated Algebraic Formulation
8.5.2 Momentum/Energy Conservation
9.
Computational Fluid Dynamics on a Staggered Grid
9.1 Challenges in the CFD Development
9.1.2 Equation for Pressure
9.1.3 Pressure-Velocity Decoupling
9.2 A Staggered Grid: One of the First Strategy to avoid Pressure-Velocity Decoupling
9.3 Physical Law based FVM for a Staggered Grid
9.4 Flux based Solution Methodology on a Uniform Grid: Semi-Explicit Method
9.4.1 Philosophy of Pressure-Correction Method
9.4.2 Semi-Explicit Method
9.4.3 Implementation Details
9.5 Initial and Boundary Conditions
10.
Computational Fluid Dynamics on a Co-located Grid
10.1 Momentum-Interpolation Method: Strategy to avoid the Pressure-Velocity Decoupling on a Col-ocated Grid
10.2 Coefficients of LAEs based Solution Methodology on a Non-Uniform Grid: Semi-Explicit and Semi-Implicit Method
10.2.3 Solution Algorithm
Part III. CFD FOR A COMPLEX-GEOMETRY
11.
Computational Heat Conduction on a Curvilinear Grid
11.1 Curvilinear Grid Generation
11.1.1 Algebraic Grid Generation
11.1.2 Elliptic Grid Generation
11.2 Physical Law based Finite Volume Method
11.2.1 Unsteady and Source Term
11.3 Computation of Geometrical Properties
11.4 Flux based Solution Methodology
11.4.2 Implementation Details
12.
Computational Fluid Dynamics on a Curvilinear Grid
12.1 Physical Law based Finite Volume Method
12.1.2 Momentum Conservation
12.2 Solution Methodology: Semi-Explicit Method
Introduction to Computational Fluid Dynamics
：Development, Application and Analysis
( Ane/Athena Books )
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