Lectures on Computational Fluid Dynamics, Mathematical Physics, and Linear Algebra

by Gustafson, Karl E.; Abe, T.; Kuwahara, K.

• ISBN13: 9789810232139
• ISBN10: 9810232136
• Format: Hardcover
• Copyright: 1998-04-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Table of Contents

Introduction	3	(4)
Part I. Recent Developments in Computational Fluid Dynamics	7	(47)
Perspective	7	(1)
Chapter 1 Cavity Flow	8	(9)
1.1. CFD Short Course	8	(2)
1.2. A Computational Benchmark Problem	10	(4)
1.3. Hopf Bifurcation	14	(3)
Chapter 2 Hovering Aerodynamics	17	(8)
2.1. Biological Motivations	17	(1)
2.2. Computational Model	18	(3)
2.3. Vortex Dynamics and Lift	21	(4)
Chapter 3 Capturing Correct Solutions	25	(29)
3.1. Numerical Rotational Release	25	(5)
3.2. Vorticity in the Far Field	30	(6)
3.3. Splitting Errors	36	(3)
Comments and Bibliography	39	(8)
References	47	(7)
Part II. Recent Developments in Mathematical Physics	54	(69)
Perspective	54	(1)
Chapter 1 Probabilistic and Deterministic Description	55	(22)
1.1. Theories of Prigogine and Kolmogorov	55	(6)
1.2. Three Converses	61	(7)
1.3. Irreversibility and Second Laws	68	(9)
Chapter 2 Scaling Theories	77	(12)
2.1. Multiresolution Analyses	77	(6)
2.2. Wavelets and Stochastic Processes	83	(3)
2.3. The Time Operator of Wavelets	86	(3)
Chapter 3 Chaos in Iterative Maps	89	(34)
3.1. Attractors and Repellers	89	(2)
3.2. A Gap Theory for Information Dimension	91	(11)
3.3. Onset of Chaos in Neural Learning	102	(6)
Comments and Bibliography	108	(4)
References	112	(11)
Part III. Recent Developments in Linear Algebra	123
Perspective	123	(1)
Chapter 1 Operator Trigonometry	124	(9)
1.1. Semigroup Generators	124	(2)
1.2. Cos A and Sin A	126	(1)
1.3. The Min-Max Theorem	127	(6)
Chapter 2 Antieigenvalues	133	(8)
2.1. Variational Formulation	133	(1)
2.2. The Euler Equation	134	(3)
2.3. Kantorovich-Wielandt Inequalities	137	(4)
Chapter 3 Computational Linear Algebra	141
3.1. Optimization Algorithms	141	(5)
3.2. Iterative Solvers for Ax = b	146	(3)
3.3. Preconditioning Numbers	149	(4)
Comments and Bibliography	153	(3)
References	156