Introduction to Computational Fluid Dynamics: Development, Application and Analysis

Description

This more-of-physics, less-of-math, insightful and comprehensive book simplifies computational fluid dynamics for readers with little knowledge or experience in heat transfer, fluid dynamics or numerical methods. The novelty of this book lies in the simplification of the level of mathematics in CFD by presenting physical law (instead of the traditional differential equations) and discrete (independent of continuous) math-based algebraic formulations. Another distinguishing feature of this book is that it effectively links theory with computer program (code). This is done with pictorial as well as detailed explanations of implementation of the numerical methodology. It also includes pedagogical aspects such as end-of-chapter problems and carefully designed examples to augment learning in CFD code-development, application and analysis. This book is a valuable resource for students in the fields of mechanical, chemical or aeronautical engineering. Foreword Preface Contents About the Author Part I Introduction and Essentials 1 Introduction 1.1 CFD: What Is It? 1.1.1 CFD as a Scientific and Engineering Analysis Tool 1.1.2 Analogy with a Video Camera 1.2 CFD: Why to Study? 1.3 Novelty, Scope, and Purpose of This Book References 2 Introduction to CFD: Development, Application, and Analysis 2.1 CFD Development 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 2.1.5 Testing 2.2 CFD Application 2.3 CFD Analysis 2.4 Closure References 3 Essentials of Fluid Dynamics and Heat Transfer for CFD 3.1 Physical Laws 3.1.1 Fundamental/Conservation Laws 3.1.2 Subsidiary Laws 3.2 Momentum and Energy Transport Mechanisms 3.3 Physical Law-Based Differential Formulation 3.3.1 Continuity Equation 3.3.2 Transport Equations 3.4 Generalized Volumetric and Flux Terms, and Their Differential Formulation 3.4.1 Volumetric Term 3.4.2 Flux-Term 3.4.3 Discussion 3.5 Mathematical Formulation 3.5.1 Dimensional Study 3.5.2 Non-Dimensional Study 3.6 Closure References 4 Essentials of Numerical-Methods for CFD 4.1 Finite Difference Method: A Differential to Algebraic Formulation for Governing PDE and BCs 4.1.1 Grid Generation 4.1.2 Finite Difference Method 4.1.3 Applications to CFD 4.2 Iterative Solution of System of LAEs for a Flow Property 4.2.1 Iterative Methods 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 4.4.1 Integration Rules 4.4.2 Applications to CFD 4.5 Closure References 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 5.1.3 Approximations 5.1.4 Approximated Algebraic Formulation 5.1.5 Discussion 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 LAE-based Solution Methodology on a Non-uniform Grid:Explicit and Implicit Method 5.4.1 One-Dimensional Conduction 5.4.2 Two-Dimensional Conduction References 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 6.1.3 Approximations 6.1.4 Approximated Algebraic Formulation 6.1.5 Discussion 6.2 Flux-based Solution Methodology on a Uniform Grid: Explicit Method 6.2.1 Explicit Method 6.2.2 Implementation Details 6.2.3 Solution Algorithm 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 6.3.4 Solution Algorithm References 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 7.2.1 Explicit Method 7.2.2 Implementation Details 7.2.3 Solution Algorithm 7.3 Coefficients of LAEs-based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method References 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 8.4 Approximations 8.5 Approximated Algebraic Formulation 8.5.1 Mass Conservation 8.5.2 Momentum/Energy Conservation 8.6 Closure 9 Computational Fluid Dynamics on a Staggered Grid 9.1 Challenges in the CFD Development 9.1.1 Non-Linearity 9.1.2 Equation for Pressure 9.1.3 Pressure-Velocity Decoupling 9.2 A Staggered Grid: One of the First Strategies … 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 9.4.4 Solution Algorithm 9.5 Initial and Boundary Conditions 9.5.1 Initial Condition 9.5.2 Boundary Condition References 10 Computational Fluid Dynamics on a Co-Located Grid 10.1 Momentum Interpolation Method: Strategy to Avoid the Pressure-Velocity Decoupling on a Co-Located Grid 10.2 Coefficients of LAEs-based Solution Methodology on a Non-Uniform Grid: Semi-Explicit and Semi-Implicit Method 10.2.1 Predictor Step 10.2.2 Corrector Step 10.2.3 Solution Algorithm References 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 11.2.2 Diffusion Term 11.2.3 All Terms 11.3 Computation of Geometrical Properties 11.4 Flux-based Solution Methodology 11.4.1 Explicit Method 11.4.2 Implementation Details References 12 Computational Fluid Dynamics on a Curvilinear Grid 12.1 Physical Law-based Finite Volume Method 12.1.1 Mass Conservation 12.1.2 Momentum Conservation 12.2 Solution Methodology: Semi-Explicit Method 12.2.1 Predictor Step 12.2.2 Corrector Step References Index