Ocean Acoustic Propagation by Finite Difference Methods (eBook)

Front Cover 1
Ocean Acoustic Propagation by Finite Difference Methods 4
Copyright Page 5
Table of Contents 6
Forword 8
PREFACE 10
CHAPTER 1. INTRODUCTION 12
CHAPTER 2. OCEAN ACOUSTIC WAVE PROPAGATION PROBLEMS 16
2.1. THE GOVERNING WAVE EQUATION 16
2.2. THE PARABOLIC APPROXIMATION 18
REFERENCES 23
CHAPTER 3. FINITE DIFFERENCE SCHEMES 24
3.1. FORMULATION 25
3.2. CONSISTENCY 27
3.3. STABILITY 30
REFERENCES 32
CHAPTER 4. INITIAL AND BOUNDARY CONDITIONS 34
4.1. THE INITIAL FIELD 34
4.2. A NEUMANN BOTTOM BOUNDARY CONDITION 35
4.3. INTERFACE TREATMENT 37
4.4. DISCUSSION 44
REFERENCES 46
CHAPTER 5. RANGE STEP SIZE ANALYSIS 48
5.1. THE HEAT EQUATION MODEL 48
5.2. AN EXTENSION OF THE MODEL HEAT EQUATION 50
REFERENCES 56
CHAPTER 6. WIDE-ANGLE CAPABILITY 58
6.1. RATIONAL FUNCTION APPROXIMATION 60
6.2. IFD IMPLEMENTATION 60
6.3. ESTIMATION OF THE PROPAGATION ANGLE 64
REFERENCES 67
CHAPTER 7. APPLICABLE SOLUTION METHODS OTHER THAN THE IMPLICIT FINITE DIFFERENCE SCHEME 68
7.1. THE SPLIT-STEP FOURIER ALGORITHM 68
7.2. THE NUMERICAL ORDINARY DIFFERENTIAL EQUATION METHOD 70
7.3. A STABLE EXPLICIT FINITE DIFFERENCE SCHEME 73
REFERENCES 75
CHAPTER 8. REPRESENTATIVE TEST EXAMPLES 76
8.1. BURGERS' EQUATION 76
8.2. RANGE-INDEPENDENT PROBLEMS 81
8.3. A RANGE-DEPENDENT PROBLEM 83
REFERENCES 90
CHAPTER 9. LISTING OF COMPUTER CODES 92
REFERENCE CITATION INDEX 128
SUBJECT INDEX 130
Untitled 132