An Introduction to Computational Fluid Dynamics: The Finite Volume Method

by Versteeg, H.; Malalasekra, W.

• ISBN13: 9780582218840
• ISBN10: 0582218845
• Format: Paperback
• Copyright: 2007-01-01
• Publisher: Prentice Hall

Summary

This book presents some of the fundamentals of computational fluid dynamics for the novice. It provides a thorough yet user-friendly introduction to the governing equations and boundary conditions of viscous fluid flows, turbulence and its modelling and the finite volume method of solving flow patters on a computer.

Table of Contents

Preface	ix
Acknowledgements	xi
Introduction	1	(9)
What is CFD?	1	(1)
How does a CFD code work?	2	(3)
Problem solving with CFD	5	(3)
Scope of this book	8	(2)
Conservation Laws of Fluid Motion and Boundary Conditions	10	(31)
Governing equations of fluid flow and heat transfer	10	(11)
Mass conservation in three dimensions	11	(2)
Rates of change following a fluid particle and for a fluid element	13	(1)
Momentum equation in three dimensions	14	(3)
Energy equation in three dimensions	17	(4)
Equations of state	21	(1)
Navier-Stokes equations for a Newtonian fluid	21	(3)
Conservative form of the governing equations of fluid flow	24	(1)
Differential and integral forms of the general transport equations	25	(2)
Classification of physical behaviour	27	(3)
The role of characteristics in hyperbolic equations	30	(2)
Classification method for simple partial differential equations	32	(2)
Classification of fluid flow equations	34	(1)
Auxiliary conditions for viscous fluid flow equations	35	(1)
Problems in transonic and supersonic compressible flows	36	(3)
Summary	39	(2)
Turbulence and its Modelling	41	(44)
What is turbulence?	41	(3)
Transition from laminar to turbulent flow	44	(5)
Effect of turbulence on time-averaged Navier-Stokes equations	49	(5)
Characteristics of simple turbulent flows	54	(8)
Free turbulent flows	54	(3)
Flat plate boundary layer and pipe flow	57	(5)
Summary	62	(1)
Turbulence models	62	(21)
Mixing length model	64	(3)
The k-E model	67	(8)
Reynolds stress equation models	75	(4)
Algebraic stress equation models	79	(1)
Some recent advances	80	(3)
Final remarks	83	(2)
The Finite Volume Method for Diffusion Problems	85	(18)
Introduction	85	(1)
Finite volume method for one-dimensional steady state diffusion	86	(2)
Worked examples: one-dimensional steady state diffusion	88	(11)
Finite volume method for two-dimensional diffusion problems	99	(1)
Finite volume method for three-dimensional diffusion problems	100	(2)
Summary of discretised equations for diffusion problems	102	(1)
The Finite Volume Method for Convection-Diffusion Problems	103	(32)
Introduction	103	(1)
Steady one-dimensional convection and diffusion	104	(1)
The central differencing scheme	105	(5)
Properties of discretisation schemes	110	(3)
Conservativeness	110	(2)
Boundedness	112	(1)
Transportiveness	112	(1)
Assessment of the central differencing scheme for convection-diffusion problems	113	(1)
The upwind differencing scheme	114	(6)
Assessment of the upwind differencing scheme	118	(2)
The hybrid differencing scheme	120	(4)
Assessment of the hybrid differencing scheme	123	(1)
Hybrid differencing scheme for multi-dimensional convection-diffusion	123	(1)
The power-law scheme	124	(1)
Higher order differencing schemes for convection-diffusion problems	125	(8)
Quadratic upwind differencing scheme: the QUICK scheme	125	(5)
Assessment of the QUICK scheme	130	(1)
Stability problems of the QUICK scheme and remedies	130	(2)
General comments on the QUICK differencing scheme	132	(1)
Other higher order schemes	133	(1)
Summary	133	(2)
Solution Algorithms for Pressure-Velocity Coupling in Steady Flows	135	(21)
Introduction	135	(1)
The staggered grid	136	(3)
The momentum equations	139	(3)
The SIMPLE algorithm	142	(4)
Assembly of a complete method	146	(1)
The SIMPLER algorithm	146	(2)
The SIMPLEC algorithm	148	(2)
The PISO algorithm	150	(2)
General comments on SIMPLE, SIMPLER, SIMPLEC and PISO	152	(2)
Summary	154	(2)
Solution of Discretised Equations	156	(12)
Introduction	156	(1)
The tri-diagonal matrix algorithm	157	(2)
Application of TDMA to two-dimensional problems	159	(1)
Application of the TDMA method to three-dimensional problems	159	(1)
Examples	160	(6)
Other solution techniques used in CFD	166	(1)
Summary	167	(1)
The Finite Volume Method for Unsteady Flows	168	(24)
Introduction	168	(1)
One-dimensional unsteady heat conduction	169	(5)
Explicit scheme	171	(1)
Crank-Nicolson scheme	172	(1)
The fully implicit scheme	173	(1)
Illustrative examples	174	(6)
Implicit method for two- and three-dimensional problems	180	(1)
Discretisation of transient convection-diffusion equation	181	(1)
Worked example of transient convection-diffusion using QUICK differencing	182	(4)
Solution procedures for unsteady flow calculations	186	(3)
Transient SIMPLE	186	(1)
The transient PISO algorithm	187	(2)
Steady state calculations using the pseudo-transient approach	189	(1)
A brief work on other transient schemes	189	(1)
Summary	190	(2)
Implementation of Boundary Conditions	192	(18)
Introduction	192	(2)
Inlet boundary conditions	194	(2)
Outlet boundary conditions	196	(2)
Wall boundary conditions	198	(5)
The constant pressure boundary condition	203	(2)
Symmetry boundary condition	205	(1)
Periodic or cyclic boundary condition	205	(1)
Potential pitfalls and final remarks	206	(4)
Advanced Topics and Applications	210	(30)
Introduction	210	(1)
Combustion modelling	210	(8)
The simple chemical reacting system (SCRS)	212	(3)
Eddy break-up of model of combustion	215	(1)
Laminar flamelet model	216	(2)
Calculation of buoyant flows and flows inside buildings	218	(1)
The use of body-fitted co-ordinate systems in CFD procedures	219	(3)
Advanced applications	222	(17)
Flow in a sudden pipe contraction	222	(1)
Modelling of a fire in a test room	223	(4)
Prediction of flow and heat transfer in a complex tube matrix	227	(7)
Laminar flow in a circular pipe driven by periodic pressure variations	234	(5)
Concluding remarks	239	(1)
Appendix A Accuracy of a Flow Simulation	240	(3)
Appendix B Non-uniform Grids	243	(2)
Appendix C Calculation of Source Terms	245	(2)
References	247	(8)
Index	255