Fundamentals of Computational Fluid Dynamics

Description

This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics. Front Matter....Pages I-XIV Introduction....Pages 1-5 Conservation Laws and the Model Equations....Pages 7-18 Finite-Difference Approximations....Pages 19-47 The Semi-Discrete Approach....Pages 49-65 Finite-Volume Methods....Pages 67-79 Time-Marching Methods for ODE’S....Pages 81-114 Stability of Linear Systems....Pages 115-140 Choosing a Time-Marching Method....Pages 141-152 Relaxation Methods....Pages 153-176 Multigrid....Pages 177-187 Numerical Dissipation....Pages 189-201 Split and Factored Forms....Pages 203-216 Analysis of Split and Factored Forms....Pages 217-230 Back Matter....Pages 231-249