Vignes / Vichnevetsky Numerical Mathematics and Applications

1. Auflage 2014
ISBN: 978-1-4832-9567-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 1, 433 Seiten, Web PDF

Reihe: IMACS Transactions on Scientific Computation - 85

Numerical Mathematics and Applications

Autoren/Hrsg.

Vignes, J.

Vichnevetsky, R.

Inhaltsverzeichnis

1;Front Cover;1
2;Numerical Mathematics and Applications;4
3;Copyright Page;5
4;Table of Contents;8
5;FOREWORD;6
6;Section I: ACCURACY OF COMPUTATION;14
6.1;CHAPTER 1. THE USE OF THE CESTAC METHOD IN THE PARALLEL COMPUTATION OF ROOTS OF POLYNOMIALS;16
6.1.1;I. THE CESTAC METHOD;16
6.1.2;II - THE PARALLEL COMPUTATION OF ROOTS OF POLYNOMIALS;17
6.1.3;Ill - THE INITIALIZATION AND TERMINATION OF THE ITERATIVE PROCESS;18
6.1.4;IV - THE ESTIMATION OF ACCURACY OF THE COMPUTED ROOTS;21
6.1.5;V - CONCLUSION;21
6.1.6;REFERENCES;21
6.2;CHAPTER 2. CESTAC, A TOOL FOR A STOCHASTIC ROUND-OFF ERROR ANALYSIS IN SCIENTIFIC COMPUTING;24
6.2.1;1. Introduction;24
6.2.2;2. The Arithmetic of Computers and the arising Problems;25
6.2.3;3. The Perturbation Method, Validity of a computed Result;25
6.2.4;4. The Implementation;26
6.2.5;5. CESTAC Tested on an Algorithm and Numerical Results;27
6.2.6;6. Conclusion;32
6.2.7;REFERENCES;33
6.3;CHAPTER 3. REDUCING ABBREVIATION ERRORS IN ITERATIVE RESOLUTION OF LINEAR SYSTEMS;34
6.3.1;1. INTRODUCTION;34
6.3.2;2. NOTATIONS AND THEORETICAL PROCESS;34
6.3.3;3. THE SEQUENCE OF ITERATES IN FLOATING-POINT ARITHMETIC;35
6.3.4;4. THE SET E={X : X € FN^ X=B R X + c};36
6.3.5;5. A SUFFICIENT CONDITION FOR THE EXISTENCE OF VECTORS X SOLUTIONS IN SET FN;36
6.3.6;6. CONSEQUENCES;37
6.3.7;7. VALIDITY OF COMPUTED SOLUTION;37
6.3.8;REFERENCES;38
6.4;CHAPTER 4. OPTIMAL TERMINATION CRITERION AND ACCURACY TESTS IN MATHEMATICAL PROGRAMMING;40
6.4.1;1. INTRODUCTION;40
6.4.2;2. LINEAR PROGRAMMING;40
6.4.3;3. THE KARMARKAR ALGORITHM [ 3 ];42
6.4.4;4. CONSTRAINED NON-LINEAR PROGRAMMING;44
6.4.5;5. REFERENCES;44
6.5;CHAPTER 5. ON THE USE OF THE NORMED RESIDUE TO CHECK THE QUALITY OF THE SOLUTION OF A LINEAR SYSTEM;46
6.5.1;ABSTRACT;46
6.5.2;0. INTRODUCTION;46
6.5.3;1. NOTATIONS AND HYPOTHESIS;46
6.5.4;2. ANALYSIS OF RELATIVE ERRORS;47
6.5.5;3 - NUMBER OF EXACT DIGITS;48
6.5.6;4. - INCIDENCE OF ROUNDING ERRORS;49
6.5.7;5. COMPARISON WITH THE NORMED RESIDUE;50
6.5.8;6 - EXAMPLE;50
6.5.9;7 - CONCLUSION;52
6.5.10;REFERENCES;52
6.6;CHAPTER 6. COMPUTABLE BOUNDS FOR SOLUTIONS OF INTEGRAL EQUATIONS;54
6.6.1;INTEGRAL EQUATIONS;54
6.6.2;INTERVAL ANALYSIS;54
6.6.3;INTERVAL INTEGRATION;55
6.6.4;INTERVAL ITERATION;55
6.6.5;INCLUSION OF INTEGRAL OPERATORS;55
6.6.6;MONOTONICITY METHODS;56
6.6.7;DIRECTED ROUNDING;56
6.6.8;ITERATIVE RESIDUAL CORRECTION;56
6.6.9;EIGENVALUE PROBLEMS;57
6.6.10;REFERENCES;58
6.7;CHAPTER 7. Arbitrarily Accurate Boundaries for Solutions of ODEs with Initial Values using Variable Precision Arithmetic;60
6.7.1;Abstract;60
6.7.2;1 Introduction;60
6.7.3;2 The Multi Level Structure;60
6.7.4;3 Elements of the Numerical Basis;61
6.7.5;4 The Initial Value Problem;62
6.7.6;5 The Algorithm;63
6.7.7;6 The Inclusion of the Solution;65
6.7.8;7 Conclusions;66
6.7.9;References;66
7;Section II: APPROXIMATIONS AND ALGORITHMS;68
7.1;CHAPTER 8. REMARKS ON SOME MODIFIED ROMBERG ALGORITHMS FOR NUMERICAL INTEGRATION;70
7.1.1;SUMMARY;70
7.1.2;1. INTRODUCTION;70
7.1.3;2. PROBLEM FORMULATION;70
7.1.4;3. EXTRAPOLATION SCHEMES;73
7.1.5;4. SOME REMARKS ON THE IMPLEMENTATION OF THE ALGORITHM;75
7.1.6;5. NUMERICAL EXPERIMENTS;76
7.1.7;REFERENCES;76
7.2;CHAPTER 9. LINEAR AND QUASILINEAR EXTRAPOLATION ALGORITHMS;78
7.2.1;0. INTRODUCTION, NOTATION AND DEFINITIONS;78
7.2.2;1. A GENERAL DETERMINANTAL IDENTITY;78
7.2.3;2. RECURRENCE FORMULAS FOR EXTRAPOLATION;79
7.2.4;3. PARTICULAR CASES AND APPLICATIONS;81
7.2.5;REFERENCES;83
7.3;CHAPTER 10. VECTOR PADÉ APPROXIMANTS;86
7.3.1;NATURE OF THE PROBLEM;86
7.3.2;I - PADÉ-TYPE APPROXIMANTS;86
7.3.3;II - IMPROVEMENT OF THE ORDER OF APPROXIMATION;87
7.3.4;Ill - DENOMINATORS OF THE VECTOR PADÉ APPROXIMANTS;87
7.3.5;IV- PADÉ APPROXIMANTS AS RATIO OF TWO DETERMINANTS;88
7.3.6;V - RECURSIVE COMPUTATION OF THE VECTOR PADÉ-APPROXIMANTS;89
7.3.7;REFERENCES;90
7.4;CHAPTER 11. THREE COMPUTATIONAL ASPECTS OF CONTINUED FRACTION/PADÉ APPROXIMANTS;92
7.4.1;1. INTRODUCTION;92
7.4.2;1. SPEED OF CONVERGENCE AND A PRIORI TRUNCATION ERROR ESTIMATES;94
7.4.3;2. ACCELERATION OF CONVERGENCE;95
7.4.4;3. ANALYTIC CONTINUATION AND NUMERICAL STABILITY;96
7.4.5;REFERENCES;97
7.5;CHAPTER 12. AN UNIVERSAL CONVERSATIONAL PROGRAM FOR COMPUTING SEQUENCES OF PADE APPROXIMANTS IN THE NON NORMAL CASE;98
7.5.1;SUMMARY;98
7.5.2;1. THE NORMAL CASE;98
7.5.3;2. THE NON NORMAL CASE;99
7.5.4;3. THE CONVERSATIONAL PROGRAM [5];99
7.5.5;4. NUMERICAL EXAMPLE [6];100
7.5.6;5 - CONCLUSION;100
7.5.7;BIBLIOGRAPHY;100
7.6;CHAPTER 13. EFFICIENT COMPUTATION OF A GROUP OF CLOSE EIGENVALUES FOR INTEGRAL OPERATORS;102
7.6.1;ABSTRACT;102
7.6.2;1. INTRODUCTION;102
7.6.3;2. THEORETICAL ASPECTS;102
7.6.4;3. PRACTICAL COMPUTATIONS;104
7.6.5;4. NUMERICAL EXAMPLES;105
7.6.6;5. FINAL REMARKS;105
7.6.7;REFERENCES;106
7.7;CHAPTER 14. Data Flow Analysis of Orthogonal Properties on the Conjugate Gradient and the Lanczos Algorithm;108
7.7.1;1. Introduction;108
7.7.2;2. The Conjugate Gradient and Lanczos Method;108
7.7.3;3. Propagation of Orthogonality;110
7.7.4;4. Numerical Experiments;111
7.7.5;Acknowledgment;112
7.7.6;References;112
8;Section III: SOLUTION OF ODE'S AND PDE'S;118
8.1;CHAPTER 15. EFFICIENT PRECONDITIONINGS FOR MATRIX PROBLEMS RESULTING FROM HIGH ORDER METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS;120
8.1.1;1. INTRODUCTION;120
8.1.2;2. PRECONDITIONING TECHNIQUES;122
8.1.3;3. SOLUTION PROCEDURES;123
8.1.4;4. NUMERICAL RESULTS;124
8.1.5;5. CONCLUSIONS;127
8.1.6;ACKNOWLEDGEMENT;128
8.1.7;REFERENCES;128
8.2;CHAPTER 16. VARIABLE STEP SIZE / VARIABLE ORDER PDE SOLVER WITH GLOBAL OPTIMISATION;130
8.2.1;1. INTRODUCTION;130
8.2.2;2. ACCESS TO THE ERROR;130
8.2.3;3. COMPUTATIONAL AMOUNT;131
8.2.4;4. SELECTION OF THE ORDER;132
8.2.5;5. SELECTION OF THE LOCAL STEP SIZES;133
8.2.6;6. FURTHER REMARKS TO THE CONTROL;134
8.2.7;7. EXAMPLES;134
8.2.8;Acknowledgement;135
8.2.9;8. REFERENCES;135
8.3;CHAPTER 17. APPROXIMATE PRACTICAL STABILITY FOR NONLINEAR EVOLUTION PDES;138
8.3.1;1. INTRODUCTION;138
8.3.2;2. THE PROBLEM FROM CONTINUUM MECHANICS;139
8.3.3;3. THE SPECIAL CASE OF THE LINEAR PDES;141
8.3.4;4. ON FOURIER-POLYNOMIALS FOR THE APPROXIMATION OF v, e, AND s;142
8.3.5;5. APPLICATION OF THE MEAN VALUE INTERVAL METHOD;142
8.3.6;6. THE ENCLOSURE CONDITION;143
8.3.7;7. THE NONLINEAR SAMPLE PROBLEM;144
8.3.8;8. INVESTIGATION CONCERNING INDIVIDUAL FOURIER-MODES;144
8.3.9;9. NUMERICAL RESULTS FOR THE SYSTEM (7.4);145
8.3.10;10. CONCLUSIONS;146
8.3.11;REFERENCES;147
8.4;CHAPTER 18. CURRENT METHODS FOR LARGE STIFF ODE SYSTEMS;148
8.4.1;1. INTRODUCTION;148
8.4.2;2. SOLUTION METHOD TYPES;149
8.4.3;3. RECENT DEVELOPMENTS;151
8.4.4;REFERENCES;155
8.5;CHAPTER 19. EXPONENTIAL-FITTED METHODS FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS;158
8.5.1;1. INTRODUCTION;158
8.5.2;2. THE PROBLEM OF STIFFNESS;158
8.5.3;3. EXPONENTIAL-BASED ALGORITHMS;159
8.5.4;4. LOCAL ERROR ESTIMATES;161
8.5.5;5. DISCUSSION AND CONCLUSIONS;163
8.5.6;REFERENCES;164
8.6;CHAPTER 20. LINEARIZED D-MAPPING FOR STIFF COMPUTATIONS;166
8.6.1;1. INTRODUCTION;166
8.6.2;2. D-MATRIX AND D-MAPPING;166
8.6.3;3. LINEARIZED D-MAPPING ANALYSIS;166
8.6.4;4. CONVEX-TYPE OPERATION;167
8.6.5;5. AN APPLICATION;167
8.6.6;6. DISCUSSIONS;168
8.6.7;REFERENCES;168
8.7;CHAPTER 21. ON THE USE OF NEWTON'S METHOD IN THE ADAPTIVE SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS;170
8.7.1;1. Introduction;170
8.7.2;2. Preliminaries;170
8.7.3;3. Coarse-Fine Grid Relationship;171
8.7.4;4. Estimation of the Newton Kantorovich Norms;172
8.7.5;5. Assessment of the Convergence Estimates;172
8.7.6;6. Numerical Results;173
8.7.7;References;174
8.8;CHAPTER 22. SPLINE APPROXIMATIONS IN NUMERICAL METHOD OF LINES SOLUTION OF FIRST-ORDER HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS;176
8.8.1;1. INTRODUCTION;176
8.8.2;2. TEST PROBLEM;177
8.8.3;3. SPLINE DIFFERENTIATOR;177
8.8.4;4. HYBRIDIZED SPLINE;179
8.8.5;5. ADAPTIVE GRID;179
8.8.6;6. HYBRIDIZED ADAPTIVE GRID;181
8.8.7;7. CONCLUSIONS;181
8.8.8;NOTATION;181
8.8.9;SUBSCRIPTS;183
8.8.10;REFERENCES;183
8.9;CHAPTER 23. SOME INSIGHTS INTO THE STABILITY OF DIFFERENCE APPROXIMATIONS FOR HYPERBOLIC INITIAL-BOUNDARY-VALUE PROBLEMS;184
8.9.1;1. Introduction;184
8.9.2;2. IBVP for a model hyperbolic equation;184
8.9.3;3. A prototype difference scheme for the model IBVP;185
8.9.4;4. Lax-Richtmyer stability of a discrete IBVP;185
8.9.5;5. Difficulties in proving Lax-Richtmyer stability;186
8.9.6;6. Normal-mode analysis (quarter-plane problems);186
8.9.7;7. A conjecture on a test forLax-Richtmyer stability;187
8.9.8;References;189
8.10;CHAPTER 24. USE OF A DYNAMIC GRID ADAPTION IN THE ASWR-METHOD;190
8.10.1;1. SUMMARY;190
8.10.2;2. INTRODUCTION;190
8.10.3;3. THE ASWR-METHOD ON A NONUNIFORM GRID;191
8.10.4;4. PRACTICAL CONSIDERATIONS;192
8.10.5;5. EXAMPLE;193
8.10.6;6. CONCLUSION;193
8.10.7;REFERENCES;194
8.11;CHAPTER 25. THE SOLUTION OF AN ELLIPTIC P.D.E. WITH PERIODIC BOUNDARY CONDITIONS IN A RECTANGULAR REGION;198
8.11.1;1. INTRODUCTION;198
8.11.2;2. PROBLEM DEFINITION;198
8.11.3;3. THE SOLUTION OF CONSTANT TERM CYCLIC TRIDIAGONAL MATRIX SYSTEMS;199
8.11.4;4. THE CYCLIC BLOCK FACTORISATION METHOD;200
8.11.5;5. THE SPECTRAL RESOLUTION METHOD;203
8.11.6;6. NUMERICAL EXPERIMENTS;204
8.11.7;REFERENCES;205
8.12;CHAPTER 26. A MODIFIED GALERKIN SCHEME FOR ELLIPTIC EQUATIONS WITH NATURAL BOUNDARY CONDITIONS;206
8.12.1;1. INTRODUCTION;206
8.12.2;2. BOUNDARY VALUE PROBLEMS;206
8.12.3;3. GALERKIN APPROXIMATIONS;209
8.12.4;4. CONCLUDING REMARKS;209
8.12.5;REFERENCES;210
8.13;CHAPTER 27. NUMERICAL GRID GENERATION THROUGH SECOND ORDER DIFFERENTIAL-GEOMETRIC MODELS;212
8.13.1;SUMMARY;212
8.13.2;INTRODUCTION;212
8.13.3;BASIC ELLIPTIC MODELS;212
8.13.4;NUMERICAL RESULTS;214
8.13.5;ACKNOWLEDGEMENT;216
8.13.6;REFERENCES;216
8.14;CHAPTER 28. FACTORIZATION AND PATH INTEGRATION OF THE HELMHOLTZ EQUATION: NUMERICAL ALGORITHMS;218
8.14.1;1. INTRODUCTION;218
8.14.2;2. FACTORIZATION AND PATH INTEGRATION;218
8.14.3;3. COMPUTATIONAL ALGORITHM;219
8.14.4;4. NUMERICAL RESULTS;220
8.14.5;5. DISCUSSION;220
8.14.6;6. REFERENCES;224
8.15;CHAPTER 29. A GENERAL ERGUN EQUATION FOR A MJLTILAYERED POROUS MEDIUM;226
8.15.1;1. INTRODUCTION;226
8.15.2;2. SUMMARY OF EXISTING THEORY;226
8.15.3;3. THE ANISOTROPIC APPROACH;228
8.15.4;4. CONCLUSION;232
8.15.5;5. LIST OF SYMBOLS;232
8.15.6;REFERENCES;233
8.16;CHAPTER 30. ITERATIVE SOLUTIONS OF PROBLEMS WITH SHOCKS;234
8.16.1;SUMMARY;234
8.16.2;1. NEWTON'S METHOD;234
8.16.3;2. TWO LEVEL ITERATIVE METHODS OF GRADIENT TYPE;234
8.16.4;3. THE BURGERS EQUATION;237
8.16.5;4. THE TRANSONIC SMALL DISTURBANCE EQUATION;240
8.16.6;5. CONCLUSION;242
8.16.7;ACKNOWLEDGEMENTS;243
8.16.8;REFERENCES;243
8.17;CHAPTER 31. THE LUMPED MASS FINITE ELEMENT METHOD FOR PARABOLIC EQUATIONS;244
8.17.1;SUMMARY;244
8.17.2;References;246
8.18;CHAPTER 32. THE SOLUTION OF BURGERS' EQUATION BY BOUNDARY VALUE METHODS;248
8.18.1;Abstract;248
8.18.2;1. Introduction;248
8.18.3;2. The Boundary Value Procedure;248
8.18.4;3· Iterative Methods of Solution;248
8.18.5;4. Iterative Methods of Solution;249
8.18.6;5. The Hopscotch Formulation of the Boundary Value Technique;250
8.18.7;6. Numerical Experiments;251
8.18.8;7. Conclusions;251
8.18.9;References;252
9;Section IV: COMPUTATIONAL ACOUSTICS;254
9.1;CHAPTER 33. NUMERICAL MODELS FOR OCEAN ACOUSTIC MODES;256
9.1.1;1. INTRODUCTION;256
9.1.2;2. SUMMARY OF THE NUMERICAL METHOD FOR THE STANDARD NORMAL MODE PROBLEM (1.1);257
9.1.3;3. RESULTS;258
9.1.4;REFERENCES;258
9.2;CHAPTER 34. THE RELATION OF THE PARABOLIC EQUATION METHOD TO THE ADIABATIC MODE APPROXIMATION;262
9.2.1;1. INTRODUCTION;262
9.2.2;2. BASIC PROPAGATION PROBLEM;263
9.2.3;3. COUPLED MODES;263
9.2.4;4. ADIABATIC APPROXIMATIONS;264
9.2.5;5. ADIABATIC EQUIVALENCES;265
9.2.6;6. NATURAL REFERENCE WAVENUMBER;266
9.2.7;7. CONSTANT REFERENCE WAVENUMBER;267
9.2.8;8. CONCLUDING REMARKS;267
9.2.9;ACKNOWLEDGMENTS;267
9.2.10;REFERENCES;267
9.3;CHAPTER 35. A SURVEY OF NUMERICAL METHODS FOR A NEW CLASS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ARISING IN NONSPHERICAL GEOMETRICAL OPTICS;270
9.3.1;1. INTRODUCTION: FORMULATION OF THE GENERAL EQUATIONS ;270
9.3.2;2. BOUNDARY VALUE PROBLEMS AND SOLUTION METHODS;271
9.3.3;3. EXISTENCE THEORY AND QUESTIONS;274
9.3.4;REFERENCES;275
9.4;CHAPTER 36. WIDE ANGLE PARABOLIC APPROXIMATIONS IN UNDERWATER ACOUSTICS;278
9.4.1;1. INTRODUCTION;278
9.4.2;2. COMPARISON OF PROPAGATION ANGLES;279
9.4.3;3. A NEW WIDE ANGLE PARABOLIC APPROXIMATION;280
9.4.4;4. TIME-DEPENDENT ONE-WAY WAVE EQUATIONS;283
9.4.5;ACKNOWLEDGEMENT;284
9.4.6;REFERENCES;284
9.5;CHAPTER 37. THE APPLICATION OF THE BOUNDARY INTEGRAL ELEMENT METHOD TO THE PROBLEM OF SCATTERING OF SOUND WAVES BY AN ELASTIC WEDGE;286
9.5.1;SUMMARY;286
9.5.2;FORMULATION OF THE PROBLEM;286
9.5.3;THE METHOD OF SOLUTION;287
9.5.4;SOME RESULTS;290
9.5.5;CONCLUSIONS;292
9.5.6;REFERENCES;292
9.5.7;ACKNOWLEDGEMENTS;292
9.6;CHAPTER 38. A WAVE PROPAGATION COMPUTATION TECHNIQUE USING FUNCTION THEORETIC REPRESENTATION;294
9.6.1;1. INTRODUCTION;294
9.6.2;2. TRANSMUTATION FROM IDEALIZED TO PERTURBED;294
9.6.3;3. THE BOUNDARY CONDITION AT z=b IS PRESERVED;295
9.6.4;4. SOME BOUNDARY TYPE CONDITIONS FOR THE KERNEL;295
9.6.5;5. DERIVATION OF THE PARTIAL DIFFERENTIAL EQUATION AND CONDITIONS THAT THE KERNEL MUST SATISFY;296
9.6.6;6. THE OTHER BOUNDARY CONDITION IS NOT PRESERVED;296
9.6.7;7. EXISTENCE AND UNIQUENESS OF THE TRANSMUTATION;297
9.6.8;8. FINDING GREEN'S FUNCTION BY HANKEL TRANSFORM;297
9.6.9;9. A SPECIAL EXAMPLE OF THE TRANSMUTATION KERNEL;298
9.6.10;10. FINDING KERNEL APPROXIMATIONS USING MACSYMA;299
9.6.11;ACKNOWLEDGEMENT;301
9.6.12;FOOTNOTES;301
9.6.13;REFERENCES;301
9.7;CHAPTER 39. COMPENSATING FOR WAVEFRONT TURNING IN WAVEFRONT CURVATURE RANGING;302
9.7.1;1. INTRODUCTION;302
9.7.2;2. CONVENTIONAL TRIANGULATION;302
9.7.3;3. WAVEFRONT TURNING "AT ENDFIRE";303
9.7.4;4. WHAT CAN BE ACHIEVED AT ENDFIRE;304
9.7.5;5. MEASURING WAVEFRONT CURVATURE AT ENDFIRE;304
9.7.6;6. "NORMAL" RADIUS OF CURVATURE APPROXIMATES RANGE;305
9.7.7;7. CONCLUSIONS;305
9.7.8;ACKNOWLEDGMENT;306
9.7.9;REFERENCES;306
9.8;CHAPTER 40. CHANGES IN EIGENVALUES DUE TO BOTTOM INTERACTION USING PERTURBATION THEORY;308
9.8.1;1. INTRODUCTION;308
9.8.2;2. FORMULATION;308
9.8.3;3. PERTURBATION;309
9.8.4;4. EXAMPLES;311
9.8.5;ACKNOWLEDGEMENT;313
9.8.6;REFERENCES;314
10;Section V: COMPUTATIONAL FLUID DYNAMICS;316
10.1;CHAPTER 41. COMPUTATIONAL FLUID DYNAMICS, CONVERGENT OR ASYMPTOTIC;318
10.1.1;1. INTRODUCTION;318
10.1.2;2. NONLINEAR EQUIVALENCE THEOREM;319
10.1.3;3. ERROR ANALYSIS;320
10.1.4;4. ASYMPTOTICS;321
10.1.5;5. CONCLUDING REMARKS;322
10.1.6;ACKNOWLEDGEMENTS;322
10.1.7;REFERENCES;322
10.2;CHAPTER 42. HIGHLY ACCURATE SHOCK FLOW CALCULATIONS WITH MOVING GRIDS AND MESH REFINEMENT;324
10.2.1;1. INTRODUCTION;324
10.2.2;References;328
10.3;CHAPTER 43. MODIFIED EQUATION METHODS FOR ONE-DIMENSIONAL FLAME PROPAGATION PROBLEMS;330
10.3.1;1. INTRODUCTION;330
10.3.2;2. PROBLEM FORMULATION;331
10.3.3;3. MODIFIED EQUATION METHODS;332
10.3.4;4. STABILITY OF MODIFIED EQUATION METHODS;333
10.3.5;5. PRESENTATION OF RESULTS;335
10.3.6;6. CONCLUSIONS;338
10.3.7;REFERENCES;339
10.4;CHAPTER 44. NUMERICAL SOLUTION OF TIME-DEPENDENT INCOMPRESSIBLE FLOWS;340
10.4.1;1. INTRODUCTION;340
10.4.2;2. GOVERNING EQUATIONS AND DISCRETIZATION;340
10.4.3;3. THE NUMERICAL PROCEDURE;341
10.4.4;4. TEST PROBLEMS;341
10.4.5;5. CONCLUDING REMARKS;345
10.4.6;REFERENCES;345
10.5;CHAPTER 45. PSEUDOCHARACTERISTIC METHOD OF LINES SIMULATION OF SINGLE- AND TWO-PHASE ONE-DIMENSIONAL FLOW TRANSIENTS;346
10.5.1;1. INTRODUCTION;346
10.5.2;2. SINGLE-PHASE PROBLEM;347
10.5.3;3. TWO-PHASE PROBLEM;348
10.5.4;4. DISCUSSION;349
10.5.5;ACKNOWLEDGMENTS;349
10.5.6;REFERENCES;350
10.5.7;NOMENCLATURE;350
10.6;CHAPTER 46. LAGRANGIAN MODELING OF TURBULENT DISPERSION IN SHEAR LAYERS;352
10.6.1;1. INTRODUCTION;352
10.6.2;2. THE LAGRANGIAN APPROACH TO TURBULENT DISPERSION;352
10.6.3;3. IMPLEMENTATION AND RESULTS;354
10.6.4;4. EXTENSION TO BUOYANT CONTAMINANTS;357
10.6.5;5. CONCLUSION;358
10.6.6;ACKNOWLEDGEMENTS;358
10.6.7;REFERENCES;358
10.7;CHAPTER 47. STUDIES IN A SHALLOW WATER FLUID MODEL WITH TOPOGRAPHY;360
10.7.1;1. INTRODUCTION;360
10.7.2;2. NUMERICAL MODEL;360
10.7.3;3. NUMERICAL SIMULATIONS;361
10.7.4;4. PHASE SPEED;362
10.7.5;REFERENCES;364
10.7.6;APPENDIX;364
10.8;CHAPTER 48. COMPUTATION OF THE FINE VORTEX STRUCTURES OF FLUIDS;368
10.8.1;1. INTRODUCTION;368
10.8.2;2. FLUID FINE VORTEX STRUCTURE RESULTS;370
10.8.3;3. ROBUST COMPUTATION OF FLUID FINE STRUCTURE;373
10.8.4;4. ADDITIONAL REMARKS;374
10.8.5;ACKNOWLEDGEMENTS;375
10.8.6;REFERENCES;375
10.9;CHAPTER 49. INVISCID VORTEX FLOW SIMULATIONS BY MEGACELL SOLUTIONS TO THE EULER EQUATIONS;378
10.9.1;Summary;378
10.9.2;Introduction;378
10.9.3;Numerical Solution Procedure;378
10.9.4;Simulated Supersonic Vortex Flowfields;379
10.9.5;References;379
10.10;CHAPTER 50. TRANSONIC POTENTIAL FLOWS: IMPROVED ACCURACY BY USING LOCAL GRIDS;382
10.10.1;SUMMARY;382
10.10.2;1. INTRODUCTION;382
10.10.3;2. GOVERNING EQUATIONS AND FINITE-DIFFERENCE APPROXIMATION;382
10.10.4;3. LOCAL MESH REFINEMENTS;383
10.10.5;4. NUMERICAL RESULTS;384
10.10.6;REFERENCES;388
10.11;CHAPTER 51. NUMERICAL ANALYSIS OF UNSTEADY WAKE DEVELOPMENT BEHIND AN IMPULSIVELY STARTED CYLINDER IN SLIGHTLY VISCOUS FLUID;390
10.11.1;Abstract;390
10.11.2;1. Introduction;390
10.11.3;2. The Numerical Method in 2-D;390
10.11.4;3. Numerical Parameters;392
10.11.5;4. Evolution of the Vorticity Peak;393
10.11.6;5. Development of 'Vortex' Structures in the Recirculating Zones;393
10.11.7;6. Calculated Numerical Functionals;396
10.11.8;7. Conclusion;398
10.11.9;References;398
10.12;CHAPTER 52. NUMERICAL TREATMENT OF SHOCKS IN UNSTEADY POTENTIAL FLOW COMPUTATION;400
10.12.1;ABSTRACT;400
10.12.2;1. INTRODUCTION;400
10.12.3;2. ONE-DIMENSIONAL SHOCK WAVE MOTION;400
10.12.4;3. TWO-DIMENSIONAL UNSTEADY TRANSONIC POTENTIAL FLOW;403
10.12.5;REFERENCES;405
10.13;CHAPTER 53. GENERALIZED VORTEX METHODS FOR STRATIFIED LAYERED FLOWS;406
10.13.1;1. STRATIFIED VORTEX FLOWS;406
10.13.2;2. INTERFACIAL FLOW;406
10.13.3;3. NUMERICAL TECHNIQUES;407
10.13.4;4. APPLICATIONS;407
10.13.5;5. COMMENTS AND CONCLUSIONS;409
10.13.6;REFERENCES;409
10.14;CHAPTER 54. A TWO-FLUID MODEL OF TURBULENCE APPLIED TO SIMULATION OF FIRES;412
10.14.1;Abstract;412
10.14.2;Introduction;412
10.14.3;The Physical Process Considered;413
10.14.4;The Simulated Physical Process;413
10.14.5;The Differential Equations Conservation of Mass;413
10.14.6;Conservation of a General Dependent Variable;413
10.14.7;The Interfluid Relations Interfluid Mass Transfer;413
10.14.8;Interfluid Friction;414
10.14.9;The Modelling of Turbulence;414
10.14.10;The Combustion Model;415
10.14.11;The Second-Fluid Density;415
10.14.12;Parametric Studies;415
10.14.13;Results;415
10.14.14;Computer Requirements;418
10.14.15;Conclusions;418
10.14.16;References;418
10.15;CHAPTER 55. NUMERICAL PREDICTION OF TURBULENT FLOW OVER A SURFACE-MOUNTED CUBE;420
10.15.1;Summary;420
10.15.2;Introduction;420
10.15.3;Experiment;420
10.15.4;Mathematical Formulation;421
10.15.5;Method of Solution;422
10.15.6;Computational Detail;423
10.15.7;Presentation and Discussion of Results;423
10.15.8;Conclusions;424
10.15.9;References;424
10.16;CHAPTER 56. NUMERICAL MODELLING OF AIR FLOW IN CONFINED TAPERED DUCT INLETS;428
10.16.1;1. INTRODUCTION;428
10.16.2;2. MATHEMATICAL MODELLING;428
10.16.3;3. NUMERICAL PROCEDURE;428
10.16.4;4. BOUNDARY CONDITIONS;429
10.16.5;5. COMPUTATION OF THE POTENTIAL FLOW FIELD;429
10.16.6;6. NUMERICAL RESULTS;430
10.16.7;7. DISCUSSION;432
10.16.8;REFERENCES;433
10.17;CHAPTER 57. SUBSURFACE FLUID DYNAMICS AND TRANSPORT PHENOMENA BASED ON A VECTOR REPRESENTATION;434
10.17.1;1. INTRODUCTION;434
10.17.2;2. THEORETICAL FOUNDATIONS;434
10.17.3;3. NUMERICAL METHODS;437
10.17.4;4. THE COMPUTER PROGRAM;439
10.17.5;REFERENCES;441
11;AUTHOR INDEX;442