Introduction to Computational Fluid Dynamics

Atul Sharma, IIT Bombay, India Dr. Sharma is an Assistant Professor in the Department of Mechanical Engineering at the Indian Institute of Technology, Bombay. His main research interests include computational fluid dynamics, simulation of moving boundary problems, and simulation of convective heat transfer for external and internal flows. He currently teaches courses on Fluid Mechanics, Heat Transfer, Fluid Dynamics, Computational Methods in Thermal and Fluid Engineering, and Computational Fluid Dynamics and Heat Transfer.

I Introduction and Essentials 1


1 Introduction 3


1.1 CFD: What is it? 3


1.2 CFD: Why to study? 15


1.3 Novelty, Scope, and Purpose of this Book 16


2 Introduction to CFD: Development, Application, and Analysis 23


2.1 CFD Development 23


2.2 CFD Application 35


2.3 CFD Analysis 38


2.4 Closure 39


3 Essentials of Fluid-Dynamics and Heat-Transfer for CFD 41


3.1 Physical Laws 42


3.2 Momentum and Energy Transport Mechanisms 46


3.3 Physical Law based Differential Formulation 48


3.4 Generalized Volumetric and Flux Terms, and their Dif-ferential Formulation 57


3.5 Mathematical Formulation 63


3.6 Closure 71


4 Essentials of Numerical-Methods for CFD 73


4.1 Finite Difference Method: A Differential to Algebraic Formulation for Governing PDE and BCs 75


4.2 Iterative Solution of System of LAEs for a Flow Property 93


4.3 Numerical Differentiation for Local Engineering-Parameters 105


4.4 Numerical Integration for the Total value of Engineering-Parameters 110


4.5 Closure 116


II CFD for a Cartesian-Geometry 119


5 Computational Heat Conduction 121


5.1 Physical Law based Finite Volume Method 122


5.2 Finite Difference Method for Boundary Conditions 138


5.3 Flux based Solution Methodology on a Uniform Grid: Explicit-Method 139


5.4 Coe-cients of LAEs based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method 154


6 Computational Heat Advection 179


6.1 Physical Law based Finite Volume Method 180


6.2 Flux based Solution Methodology on a Uniform Grid: Explicit-Method 194


6.3 Coe-cients of LAEs based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method 207


7 Computational Heat Convection 229


7.1 Physical Law based Finite Volume Method 229


7.2 Flux based Solution Methodology on a Uniform Grid: Explicit-Method 235


7.3 Coe-cients of LAEs based Solution Methodology on a Non-Uniform Grid: Explicit and Implicit Method 242


8 Computational Fluid Dynamics: Physical Law based Finite Volume Method 251


8.1 Generalized Variables for the Combined Heat and Fluid Flow 252


8.2 Conservation Laws for a Control Volume 255


8.3 Algebraic Formulation 259


8.4 Approximations 260


8.5 Approximated Algebraic Formulation 263


8.6 Closure 269


9 Computational Fluid Dynamics on a Staggered Grid 271


9.1 Challenges in the CFD Development 273


9.2 A Staggered Grid to avoid Pressure-Velocity Decoupling 275


9.3 Physical Law based FVM for a Staggered Grid 277


9.4 Flux based Solution Methodology on a Uniform Grid: Semi-Explicit Method 281


9.5 Initial and Boundary Conditions 300


10 Computational Fluid Dynamics on a Co-located Grid 309


10.1 Momentum-Interpolation Method: Strategy to avoid the Pressure-Velocity Decoupling on a Co-located Grid 310


10.2 Coe-cients of LAEs based Solution Methodology on a Non-Uniform Grid: Semi-Explicit and Semi-Implicit Method 314


III CFD for a Complex-Geometry 331


11 Computational Heat Conduction on a Curvilinear Grid 333


11.1 Curvilinear Grid Generation 333


11.2 Physical Law based Finite Volume Method 343


11.3 Computation of Geometrical Properties 349


11.4 Flux based Solution Methodology 352


12 Computational Fluid Dynamics on a Curvilinear Grid 361


12.1 Physical Law based Finite Volume Method 361


12.2 Solution Methodology: Semi-Explicit Method 372


Problems 380


References 383


Index 389