Spectral methods for incompressible viscous flow:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2002
|
| Series: | Applied mathematical sciences
148 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 401 - 423 |
| Physical Description: | XI, 432 S. graph. Darst. |
| ISBN: | 0387952217 |
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MARC
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| 245 | 1 | 0 | |a Spectral methods for incompressible viscous flow |c Roger Peyret |
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| 500 | |a Literaturverz. S. 401 - 423 | ||
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| adam_text | ROGER PEYRET SPECTRAL METHODS FOR INCOMPRESSIBLE VISCOUS FLOW WITH 61
ILLUSTRATIONS SPRINGER CONTENTS PREFACE INTRODUCTION BASIC SPECTRAL
METHODS 7 FUNDAMENTALS OF SPECTRAL METHODS 9 1.1 GENERALITIES ON THE
METHOD OF WEIGHTED RESIDUALS 9 1.2 APPROXIMATION OF A GIVEN FUNCTION 11
1.2.1 GALERKIN-TYPE METHOD 11 1.2.2 COLLOCATION METHOD 12 1.3
APPROXIMATION OF THE SOLUTION OF A DIFFERENTIAL EQUATION . . 12 1.3.1
THE TRADITIONAL GALERKIN METHOD 13 1.3.2 THE TAU METHOD 14 1.3.3 THE
COLLOCATION METHOD 14 FOURIER METHOD 17 2.1 TRUNCATED FOURIER SERIES 17
2.1.1 CALCULATION OF FOURIER COEFFICIENTS 18 2.1.2 SOME RESULTS ON
CONVERGENCE 19 2.2 DISCRETE FOURIER SERIES 20 2.3 RELATION BETWEEN
GALERKIN AND COLLOCATION COEFFICIENTS ... 21 2.4 ODD AND EVEN
COLLOCATION 22 VIII CONTENTS 2.5 DIFFERENTIATION IN THE PHYSICAL SPACE
23 2.6 DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS 25 2.6.1
GALERKIN METHOD 25 2.6.2 COLLOCATION METHOD 26 2.7 DIFFERENTIAL EQUATION
WITH VARIABLE COEFFICIENTS 28 2.7.1 GALERKIN METHOD 28 2.7.2 COLLOCATION
METHOD 28 2.8 NONLINEAR DIFFERENTIAL EQUATION 31 2.9 ALIASING REMOVAL 33
3 CHEBYSHEV METHOD 39 3.1 GENERALITIES ON CHEBYSHEV POLYNOMIALS 40 3.2
TRUNCATED CHEBYSHEV SERIES 43 3.2.1 CALCULATION OF CHEBYSHEV
COEFFICIENTS 43 3.2.2 DIFFERENTIATION 44 3.3 DISCRETE CHEBYSHEV SERIES
AND COLLOCATION 46 3.3.1 CALCULATION OF CHEBYSHEV COEFFICIENTS 46 3.3.2
RELATION BETWEEN COLLOCATION AND GALERKIN COEFFICIENTS 48 3.3.3 LAGRANGE
INTERPOLATION POLYNOMIAL 49 3.3.4 DIFFERENTIATION IN THE PHYSICAL SPACE
50 3.3.5 ROUND-OFF ERRORS 51 3.3.6 RELATIONSHIP WITH FINITE-DIFFERENCE
AND SIMILAR APPROXIMATIONS 54 3.4 DIFFERENTIAL EQUATION WITH CONSTANT
COEFFICIENTS 55 3.4.1 TAU METHOD 56 3.4.2 COLLOCATION METHOD 59 3.4.3
ERROR EQUATION 62 3.5 DIFFERENTIAL EQUATION WITH NONCONSTANT
COEFFICIENTS 65 3.5.1 LINEAR EQUATION WITH VARIABLE COEFFICIENTS 65
3.5.2 NONLINEAR EQUATION 65 3.5.3 ALIASING 70 3.6 SOME RESULTS OF
CONVERGENCE 70 3.7 MULTIDIMENSIONAL ELLIPTIC EQUATION 77 3.7.1
ONE-DIMENSIONAL EQUATION 78 3.7.2 TWO-DIMENSIONAL EQUATION 88 3.7.3
THREE-DIMENSIONAL EQUATION 93 3.8 ITERATIVE SOLUTION METHODS 98 4
TIME-DEPENDENT EQUATIONS 101 4.1 INTRODUCTION 101 4.2 THE
ADVECTION-DIFFUSION EQUATION 104 4.2.1 THE EXACT INITIAL-BOUNDARY VALUE
PROBLEM 104 4.2.2 FOURIER APPROXIMATION 105 4.2.3 CHEBYSHEV
APPROXIMATION 106 CONTENTS IX 4.3 ONE-STEP METHOD: THE WEIGHTED
TWO-LEVEL SCHEME 110 4.3.1 FOURIER APPROXIMATION ILL 4.3.2 CHEBYSHEV
APPROXIMATION ILL 4.4 TWO-STEP METHODS 114 4.4.1 FOURIER APPROXIMATION
115 4.4.2 CHEBYSHEV APPROXIMATION 119 4.4.3 NUMERICAL ILLUSTRATION 125
4.5 HIGH-ORDER TIME-DISCRETIZATION METHODS 130 4.5.1 MULTISTEP METHODS
130 4.5.2 ONE-STEP METHODS 142 4.5.3 CONCLUSION 153 II NAVIER-STOKES
EQUATIONS 155 5 NAVIER-STOKES EQUATIONS FOR INCOMPRESSIBLE FLUIDS 157
5.1 VELOCITY-PRESSURE EQUATIONS 157 5.2 VORTICITY-STREAMFUNCTION
EQUATIONS 159 5.2.1 PLANE FLOW 159 5.2.2 AXISYMMETRIC FLOW 162 5.3
BOUSSINESQ APPROXIMATION 163 5.4 SEMI-INFINITE DOMAIN 164 6
VORTICITY-STREAMFUNCTION EQUATIONS 167 6.1 INTRODUCTION 167 6.2
FOURIER-FOURIER METHOD 168 6.3 FOURIER-CHEBYSHEV METHOD 169 6.3.1 FLOW
IN A PLANE CHANNEL 169 6.3.2 TIME-DEPENDENT STOKES EQUATIONS 170 6.3.3
NAVIER-STOKES EQUATIONS 184 6.3.4 CASE OF NONZERO FLOW RATE 186 6.4
CHEBYSHEV-CHEBYSHEV METHOD 188 6.4.1 TIME-DISCRETIZATION 188 6.4.2 THE
INFLUENCE MATRIX METHOD 188 6.4.3 OTHER INFLUENCE MATRIX METHODS 195 6.5
EXAMPLES OF APPLICATION 195 6.5.1 RAYLEIGH-BENARD CONVECTION 196 6.5.2
AXISYMMETRIC FLOW IN A ROTATING ANNULUS 202 7 VELOCITY-PRESSURE
EQUATIONS 207 7.1 INTRODUCTION 207 7.2 FOURIER-FOURIER-FOURIER METHOD
208 7.2.1 TIME-DISCRETIZATION SCHEMES 209 7.2.2 THE NONLINEAR TERM 210
7.3 FOURIER-CHEBYSHEV METHOD 212 CONTENTS 7.3.1 FLOW IN A PLANE CHANNEL
213 7.3.2 TIME-DEPENDENT STOKES EQUATIONS 213 7.3.3 NAVIER-STOKES
EQUATIONS 251 7.4 CHEBYSHEV-CHEBYSHEV METHOD 254 7.4.1 THE INFLUENCE
MATRIX METHOD 255 7.4.2 THE PROJECTION METHOD 266 7.4.3
SHEAR-STRESS-FREE BOUNDARY 277 7.4.4 ASSESSMENT OF METHODS 278 7.4.5 THE
FORM OF THE NONLINEAR TERM 286 7.5 EXAMPLE OF APPLICATION:
THREE-DIMENSIONAL FLOW IN A ROTATING ANNULUS 289 III SPECIAL TOPICS 295
8 STIFF AND SINGULAR PROBLEMS 297 8.1 INTRODUCTION 298 8.2 STIFF
PROBLEMS : COORDINATE TRANSFORMATION APPROACH .... 300 8.2.1
REQUIREMENTS 300 8.2.2 SOME TYPICAL MAPPINGS 301 8.2.3 SELF-ADAPTIVE
COORDINATE TRANSFORMATION 307 8.3 STIFF PROBLEM: DOMAIN DECOMPOSITION
APPROACH 314 8.3.1 FIXED SUBDOMAINS AND NONADAPTED COORDINATE SYSTEMS
314 8.3.2 FIXED SUBDOMAINS AND ADAPTED COORDINATE TRANSFORMATIONS 316
8.3.3 ADAPTED SUBDOMAINS AND NONADAPTED COORDINATE SYSTEMS 316 8.3.4
ADAPTED SUBDOMAINS AND ADAPTED COORDINATE TRANSFORMATIONS 317 8.4
SINGULAR PROBLEMS 321 8.4.1 SINGULAR SOLUTION OF THE LAPLACE EQUATION
323 8.4.2 NAVIER-STOKES EQUATIONS 328 8.5 FILTERING TECHNIQUE 335 9
DOMAIN DECOMPOSITION METHOD 339 9.1 INTRODUCTION 339 9.2 DIFFERENTIAL
EQUATION 341 9.2.1 PATCHING METHOD: TWO-DOMAIN SOLUTION 341 9.2.2
PATCHING METHOD : MULTIDOMAIN SOLUTION 346 9.2.3 SPECTRAL-ELEMENT METHOD
348 9.2.4 NUMERICAL ILLUSTRATION 352 9.3 TWO-DIMENSIONAL HELMHOLTZ
EQUATION 354 9.3.1 PATCHING METHOD 355 9.3.2 INFLUENCE MATRIX METHOD 357
CONTENTS XI 9.3.3 SCHUR COMPLEMENT PROBLEM 360 9.3.4 IDENTITY BETWEEN
INFLUENCE MATRIX AND SCHUR COMPLEMENT 361 9.4 TIME-DEPENDENT EQUATIONS
362 9.4.1 STABILITY OF THE CHEBYSHEV APPROXIMATION 362 9.4.2 STABILITY
OF TIME-DISCRETIZATION SCHEMES 363 9.5 NAVIER-STOKES EQUATIONS IN
VORTICITY-STREAMFUNCTION VARIABLES 365 9.5.1 FOURIER-CHEBYSHEV METHOD
365 9.5.2 CHEBYSHEV-CHEBYSHEV METHOD 368 9.5.3 EXAMPLES OF APPLICATION
371 9.6 NAVIER-STOKES EQUATION IN VELOCITY-PRESSURE VARIABLES . . . .
375 9.6.1 STOKES PROBLEM : FOURIER-CHEBYSHEV METHOD 376 9.6.2 STOKES
PROBLEM: CHEBYSHEV-CHEBYSHEV METHOD ... 378 9.6.3 EXAMPLE OF APPLICATION
385 APPENDIX A FORMULAS ON CHEBYSHEV POLYNOMIALS 389 A.I DEFINITION AND
GENERAL PROPERTIES 389 A.2 DIFFERENTIATION 390 A.3 COLLOCATION POINTS
391 A.4 TRUNCATED SERIES EXPANSION 392 A.5 LAGRANGE INTERPOLATION
POLYNOMIAL 393 A.6 DERIVATIVES AT GAUSS-LOBATTO POINTS 393 A.7
INTEGRATION 394 A.8 NUMERICAL INTEGRATION BASED ON GAUSS-LOBATTO POINTS
394 APPENDIX B SOLUTION OF A QUASI-TRIDIAGONAL SYSTEM 397 APPENDIX C
THEOREMS ON THE ZEROS OF A POLYNOMIAL 399 REFERENCES 401 INDEX 425
|
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| id | DE-604.BV014445226 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:52Z |
| institution | BVB |
| isbn | 0387952217 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009873984 |
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| owner_facet | DE-703 DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 432 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Peyret, Roger Verfasser aut Spectral methods for incompressible viscous flow Roger Peyret New York [u.a.] Springer 2002 XI, 432 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 148 Literaturverz. S. 401 - 423 Mecânica dos fluídos computacional larpcal Navier-Stokes equations Numerical solutions Spectral theory (Mathematics) Viscous flow Viskose Strömung (DE-588)4226965-9 gnd rswk-swf Inkompressible Strömung (DE-588)4129759-3 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Spektralmethode (DE-588)4224817-6 gnd rswk-swf Viskose Strömung (DE-588)4226965-9 s Inkompressible Strömung (DE-588)4129759-3 s Navier-Stokes-Gleichung (DE-588)4041456-5 s Spektralmethode (DE-588)4224817-6 s DE-604 Applied mathematical sciences 148 (DE-604)BV000005274 148 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873984&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peyret, Roger Spectral methods for incompressible viscous flow Applied mathematical sciences Mecânica dos fluídos computacional larpcal Navier-Stokes equations Numerical solutions Spectral theory (Mathematics) Viscous flow Viskose Strömung (DE-588)4226965-9 gnd Inkompressible Strömung (DE-588)4129759-3 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Spektralmethode (DE-588)4224817-6 gnd |
| subject_GND | (DE-588)4226965-9 (DE-588)4129759-3 (DE-588)4041456-5 (DE-588)4224817-6 |
| title | Spectral methods for incompressible viscous flow |
| title_auth | Spectral methods for incompressible viscous flow |
| title_exact_search | Spectral methods for incompressible viscous flow |
| title_full | Spectral methods for incompressible viscous flow Roger Peyret |
| title_fullStr | Spectral methods for incompressible viscous flow Roger Peyret |
| title_full_unstemmed | Spectral methods for incompressible viscous flow Roger Peyret |
| title_short | Spectral methods for incompressible viscous flow |
| title_sort | spectral methods for incompressible viscous flow |
| topic | Mecânica dos fluídos computacional larpcal Navier-Stokes equations Numerical solutions Spectral theory (Mathematics) Viscous flow Viskose Strömung (DE-588)4226965-9 gnd Inkompressible Strömung (DE-588)4129759-3 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Spektralmethode (DE-588)4224817-6 gnd |
| topic_facet | Mecânica dos fluídos computacional Navier-Stokes equations Numerical solutions Spectral theory (Mathematics) Viscous flow Viskose Strömung Inkompressible Strömung Navier-Stokes-Gleichung Spektralmethode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873984&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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