Mathematical modeling for complex fluids and flows:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Subjects: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3899266&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024780879&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XIX, 264 S. Ill., graph. Darst. |
| ISBN: | 9783642252945 9783642252952 364225294X |
Staff View
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 COMPLEX FLUIDS 2
1.1.1 PHYSICAL CONSIDERATIONS 3
1.1.2 VISCOELASTIC FLUIDS 5
1.1.3 VISCOMETRIC FLOWS 6
1.2 COMPLEX FLOWS 8
1.2.1 PHYSICAL CONSIDERATIONS: CIRCULAR COUETTE FLOW 8
1.2.2 TRANSITIONAL FLOWS 10
1.2.3 TURBULENT FLOWS 11
1.3 ELASTIC TURBULENCE 12
1.4 EXAMPLES OF A COMPLEX FLUID AND FLOW 12
1.4.1 THE KAYE EFFECT: SHEAR-THINNING EVIDENCE 13
1.4.2 BOUNCING NEWTONIAN JET 15
1.4.3 TURBULENT DRAG REDUCTION 15
1.5 THE MODELING MAP 17
2 TENSOR ANALYSIS, INVARIANTS, AND REPRESENTATIONS 21
2. 1 SYMMETRIES AND TRANSFORMATIONS 23
2.2 INVARIANTS AND TRACES OF MATRIX POLYNOMIALS 25
2.2.1 POLYNOMIAL INVARIANTS 26
2.2.2 TRACES OF MATRIX POLYNOMIALS 28
2.3 INTEGRITY BASES FOR VECTORS AND TENSORS 31
2.3.1 INTEGRITY BASIS FOR VECTORS 32
2.3.2 INTEGRITY BASES FOR SYMMETRIC SECOND-ORDER TENSORS . .. 32 2.3.3
INTEGRITY BASES FOR VECTORS AND SECOND-ORDER TENSORS . .. 34 2.4
POLYNOMIAL REPRESENTATIONS FOR TENSORS AND VECTORS 38
2.4.1 PROPER ORTHOGONAL GROUP 38
2.4.2 FULL ORTHOGONAL GROUP 42
3 KINEMATICS AND DYNAMICS 47
3.1 MATERIAL ELEMENTS AND DEFORMATION 47
3.1.1 DECOMPOSITION OF THE DEFORMATION 53
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1016258119
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.1.2 INFINITESIMAL STRAIN AND ROTATION 53
3.2 RATE OF DEFORMATION 55
3.2.1 TIME RATE OF CHANGE 55
3.2.2 STRAIN RATE AND ROTATION RATE TENSORS 56
3.2.3 DILATATION RATE 58
3.2.4 RIVLIN-ERICKSEN TENSORS 59
3.3 REYNOLDS TRANSPORT THEOREM 61
3.4 CONSERVATION EQUATIONS 62
3.4.1 MASS CONSERVATION 63
3.4.2 MOMENTUM CONSERVATION 63
3.4.3 ENERGY CONSERVATION 67
CONSTITUTIVE EQUATIONS: GENERAL PRINCIPLES 69
4.1 INTRODUCTION 69
4.2 METHODOLOGICAL PRINCIPLES 70
4.2.1 MATERIAL STRESS FIELD 71
4.2.2 TURBULENT STRESS FIELD 73
4.3 FRAMES, TRANSFORMATIONS AND OBJECTIVITY 75
4.3.1 TRANSFORMATIONS AND OBJECTIVITY 75
4.3.2 OBJECTIVE RATES OF THE STRESS TENSOR 79
4.4 RESTRICTIONS ON CONSTITUTIVE RELATIONSHIPS 84
4.4.1 A THERMODYNAMIC CONSTRAINT FOR CONSTITUTIVE RELATIONSHIPS 84 4.4.2
OBJECTIVITY CONSTRAINTS ON MATERIAL CONSTITUTIVE EQUATIONS 85 4.5
DEFORMATION AND CONSTANT STRETCH HISTORY MOTION 89
4.5.1 VISCOMETRIC FLOW 92
4.5.2 EXTENSIONAL FLOW 93
4.5.3 VISCOMETRIC FUNCTIONS 94
NON-NEWTONIAN AND VISCOELASTIC FLUIDS 95
5.1 INTRODUCTION 95
5.2 CLASSICAL AND GENERALIZED NEWTONIAN MODELS 96
5.2.1 NEWTONIAN FLUIDS 96
5.2.2 GENERALIZED NEWTONIAN FLUIDS 97
5.3 LINEAR VISCOELASTICITY 98
5.3.1 MAXWELL MODEL 99
5.3.2 KELVIN-VOIGT MODEL 100
5.3.3 JEFFREYS MODEL 100
5.4 FROM A SIMPLE FLUID TO VISCOELASTICITY 101
5.4.1 REINER-RIVLIN FLUID 101
5.4.2 ELASTICITY AS THE LIMIT CASE 102
5.4.3 DESIGN OF A VISCOELASTIC CONSTITUTIVE EQUATION 103 5.5
RIVLIN-ERICKSEN AND ORDER FLUIDS 103
5.5.1 RIVLIN-ERICKSEN FLUIDS 104
5.5.2 ORDER FLUIDS 104
5.5.3 PLANE SHEAR FLOW OF A SECOND-ORDER FLUID 105
5.6 CONSTANT STRETCH HISTORY FLOWS 105
IMAGE 3
CONTENTS
5.7 CONSTITUTIVE EQUATIONS OF THE RATE TYPE 107
5.7.1 OLDROYD-B MODELS 107
5.7.2 IMPROVED RATE TYPE MODELS 113
5.7.3 RELATION BETWEEN RATE TYPE AND INTEGRAL MODELS 114 5.8 DUMBBELL
MODELS 115
5.8.1 ROUSE MODEL 115
5.8.2 THE HOOKEAN DUMBBELL 116
5.8.3 DRAG FORCE 117
5.8.4 BROWNIAN MOTION 118
5.8.5 DUMBBELL STRESS 119
5.8.6 THE GIESEKUS MODEL REVISITED 121
5.9 DUMBBELLS AND STOCHASTIC DIFFERENTIAL EQUATIONS 121
5.9.1 THE FOKKER-PLANCK EQUATION 121
5.9.2 HOOKEAN DUMBBELL 123
5.9.3 NONLINEAR DUMBBELLS 124
5.9.4 DUMBBELLS WITH HYDRODYNAMIC INTERACTIONS 127
5.10 THE MICRO-MACRO DESCRIPTION 128
5.10.1 SOLVING THE FOKKER-PLANCK EQUATION 129
5.10.2 BROWNIAN CONFIGURATION FIELDS 130
5.11 CONSEQUENCES OF NON-AFFINE MOTION 130
5.11.1 DUMBBELLS WITH NON-AFFINE MOTION AND THE GORDON- SCHOWALTER MODEL
130
5.11.2 MODELING POLYMERIC NETWORKS 132
5.12 MODELING OF POLYMER MELTS 133
5.12.1 DOI-EDWARDS MODEL 134
5.12.2 DIFFERENTIAL FORM OF THE DOI-EDWARDS MODEL 137
5.12.3 POM-POM MODEL 139
5.12.4 THE EXTENDED POM-POM MODEL 143
5.12.5 LINEAR ENTANGLED POLYMER CHAINS AND THE ROLIE-POLY EQUATION 145
TURBULENT FLOWS 149
6.1 HOMOGENEITY AND THE SPECTRAL CASCADE 149
6.2 NUMERICAL SOLUTION METHODOLOGIES 152
6.2.1 DIRECT NUMERICAL SIMULATION (DNS) 154
6.2.2 SCALE RESOLVING SIMULATIONS 158
6.2.3 MEAN EQUATION METHODS 168
6.3 MEAN EQUATION CLOSURE 173
6.3.1 REYNOLDS STRESS TENSOR 175
6.3.2 DISSIPATION RATE TENSOR 179
6.4 REYNOLDS STRESS TRANSPORT EQUATION CLOSURE 183
6.4.1 PRESSURE-STRAIN RATE CORRELATION 184
6.4.2 TURBULENT TRANSPORT 188
6.5 POLYNOMIAL REPRESENTATIONS OF THE TURBULENT STRESS TENSOR . . .. 194
6.5.1 TURBULENT STRESS OF A SIMPLE FLUID 195
6.5.2 TURBULENT STRESS FROM INVARIANT BASES 197
IMAGE 4
XIV CONTENTS
6.5.3 CONSTRAINTS IMPOSED BY SOLID BOUNDARIES 210
6.6 HYBRID METHODOLOGIES 212
7 THE BOLTZMANN EQUATION 215
7.1 KINETIC THEORY 216
7.1.1 GENERALITIES 216
7.1.2 CONTINUOUS BOLTZMANN EQUATION 218
7.1.3 BOLTZMANN-BGK BASED CONTINUOUS EQUATIONS 219 7.2 HERMITE FUNCTION
APPROXIMATION 220
7.3 GALERKIN METHOD 222
7.4 CHAPMAN-ENSKOG EXPANSION 223
7.4.1 ZERO ORDER APPROXIMATION 224
7.4.2 FIRST ORDER APPROXIMATION 224
7.5 LATTICE BOLTZMANN METHOD 228
7.6 MULTIPLE RELAXATION TIME BOLTZMANN EQUATION 233
7.6.1 LINEARIZED BOLTZMANN EQUATION 233
7.6.2 MRT LATTICE BOLTZMANN METHOD 234
7.7 LBM FOR VISCOELASTIC FLUIDS 235
7.7.1 ADVECTION-DIFFUSION EQUATION WITH A SOURCE TERM 236 7.7.2
COMPUTATION OF THE CONSTITUTIVE EQUATION 238
7.7.3 DESCRIPTION OF THE ALGORITHM 239
7.8 LBM FOR TURBULENT FLOWS 240
APPENDIX PROPERTIES OF THE HERMITE POLYNOMIALS 243
CONTINUOUS CASE 243
GAUSS-HERMITE QUADRATURE RULE 245
DISCRETE CASE 246
REFERENCES 249
INDEX 261
|
| any_adam_object | 1 |
| author | Deville, Michel O. Gatski, Thomas B. |
| author_facet | Deville, Michel O. Gatski, Thomas B. |
| author_role | aut aut |
| author_sort | Deville, Michel O. |
| author_variant | m o d mo mod t b g tb tbg |
| building | Verbundindex |
| bvnumber | BV039922419 |
| classification_rvk | UF 4000 |
| ctrlnum | (OCoLC)757479571 (DE-599)DNB1016258119 |
| dewey-full | 532.05 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.05 |
| dewey-search | 532.05 |
| dewey-sort | 3532.05 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| format | Book |
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| id | DE-604.BV039922419 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:05:22Z |
| institution | BVB |
| isbn | 9783642252945 9783642252952 364225294X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024780879 |
| oclc_num | 757479571 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-83 DE-188 |
| owner_facet | DE-703 DE-11 DE-83 DE-188 |
| physical | XIX, 264 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Deville, Michel O. Gatski, Thomas B. Mathematical modeling for complex fluids and flows Nichtnewtonsche Flüssigkeit (DE-588)4139358-2 gnd Komplexe Flüssigkeit (DE-588)4311495-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| subject_GND | (DE-588)4139358-2 (DE-588)4311495-7 (DE-588)4114528-8 (DE-588)4117265-6 |
| title | Mathematical modeling for complex fluids and flows |
| title_auth | Mathematical modeling for complex fluids and flows |
| title_exact_search | Mathematical modeling for complex fluids and flows |
| title_full | Mathematical modeling for complex fluids and flows Michel O. Deville ; Thomas B. Gatski |
| title_fullStr | Mathematical modeling for complex fluids and flows Michel O. Deville ; Thomas B. Gatski |
| title_full_unstemmed | Mathematical modeling for complex fluids and flows Michel O. Deville ; Thomas B. Gatski |
| title_short | Mathematical modeling for complex fluids and flows |
| title_sort | mathematical modeling for complex fluids and flows |
| topic | Nichtnewtonsche Flüssigkeit (DE-588)4139358-2 gnd Komplexe Flüssigkeit (DE-588)4311495-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Nichtnewtonsche Flüssigkeit Komplexe Flüssigkeit Mathematisches Modell Turbulente Strömung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3899266&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024780879&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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