Multi-Level Methods in Lubrication (eBook)

A A Lubrecht, C.H. Venner (Herausgeber)

eBook Download: PDF | EPUB

2000 | 1. Auflage
400 Seiten
Elsevier Science (Verlag)
978-0-08-053709-2 (ISBN)

Infos

Efficient numerical solution of realistic and, therefore, complex equation systems occupies many researchers in many disciplines. For various reasons, but mainly in order to approximate reality, a very large number of unknowns are needed. Using classical techniques, the solution of such a system of equations would take too long, and so sometimes MultiLevel techniques are used to accelerate convergence. Over the last one and a half decades, the authors have studied the problem of Elastohydrodynamic Lubrication, governed by a complex integro-differential equation. Their work has resulted in a very efficient and stable solver. In this book they describe the different intermediate problems analyzed and solved, and how those ingredients finally come together in the EHL solver. A number of these intermediate problems, such as Hydrodynamic Lubrication and Dry Contact, are useful in their own right. In the Appendix the full codes of the Poisson problem, the Hydrodynamic Lubrication problem, the dry contact solver and the EHL solver are given. These codes are all written in 'C' language, based on the 'ANSI-C' version.

Inhalt

Front Cover 1
Multilevel Methods in Lubrication 4
Copyright Page 5
Contents 18
Foreword 8
Notation 10
Teaching 14
Chapter 1. Introdction 22
1.1 Justification 22
1.2 History 24
1.3 Description of the EHL Problem 25
1.4 Simplification 30
1.5 Model Problems 32
1.6 Conclusion 36
1.7 Advanced Topics 36
Chapter 2. Numerical Methods: Introduction 38
2.1 Model Problems 38
2.2 Discretization 39
2.3 Systems of Equations 44
2.4 Direct Solver 47
2.5 Iterative Solver 49
2.6 Relaxation 51
2.7 Performance 54
2.8 Local Mode Analysis 61
2.9 Conclusion 69
2.10 Advanced Topics 69
Chapter 3. Multigrid 78
3.1 General Principle 78
3.2 Correction Scheme 81
3.3 Intergrid Transfers 82
3.4 Coarse Grid Operator LH 92
3.5 Coarse Grid Correction Cycle 93
3.6 Cycle Performance 96
3.7 Full MultiGrid 100
3.8 Full Approximation Scheme 102
3.9 1d Results 104
3.10 2d Results 112
3.11 Conclusion 116
3.12 Advanced Techniques 117
Chapter 4. Hydrodynamic Lubrication 122
4.1 Equations 122
4.2 Discrete Equations 126
4.3 Relaxation 129
4.4 Cavitation and Complementarity 131
4.5 Coarse Grid Correction 135
4.6 Full MultiGrid 140
4.7 Accuracy 143
4.8 Other L/R Ratios: Bearing Design 145
4.9 Conclusion 149
4.10 Advanced Topics 150
Chapter 5. Dry Contact 156
5.1 Equations 156
5.2 Discrete Equations 159
5.3 Relaxation 160
5.4 Coarse Grid Correction 169
5.5 Cycle Performance 172
5.6 Full MultiGrid 174
5.7 Multilevel Multi-Integration 177
5.8 Incorporating MLMI into the FMG Solver 193
5.9 Conclusion 193
5.10 Advanced Topics 194
Chapter 6. ElastoHydrodynamic Lubrication 200
6.1 Introduction 200
6.2 Equations 201
6.3 Dimensionless Equations 202
6.4 Dimensionless Parameters 204
6.5 Discrete Equations 205
6.6 Model Problem 207
6.7 Relaxation of the EHL Problem 214
6.8 Coarse Grid Correction Cycle 221
6.9 Full MultiGrid 224
6.10 Design Graphs 231
6.11 Conclusion 233
6.12 Advanced Topics 234
Bibliography 246
Appendix A. MultiLevel Routines 256
A.1 ld Poisson Multilevel Building Blocks 256
A.2 2d Poisson Multilevel Building Blocks 260
A.3 2d Hydrodynamic Multilevel Extensions 263
A.4 2d Dry Contact Multilevel Extensions 265
A.5 2d EHL Contact Multilevel Extensions 270
Appendix B. Debugging Hints 276
B.1 MGld.c & MG2d.c
B.2 HL2d.c 277
B.3 DRY2d.c 278
B.4 EHL2d.c 279
Appendix C. Systems of Equations for Line Relaxation 280
C.1 Model Problem Small ? 280
C.2 Model Problem Varying ? 282
C.3 EHL Problem 285
Appendix D. Program Listing: MGld.c 290
Appendix E. Program Listing: MG2d.c 298
Appendix F. Program Listing: HL2d.c 310
Appendix G. Program Listing: DRY2d.c 324
Appendix H. Program Listing: EHL2d.c 344
Appendix I. Program Listing: Second Order 374
Appendix J. Program Listing: Fourth Order 378
Appendix K. Program Listing: Sixth Order 384
Appendix L. Program Listing: Eighth Order 390
Index 396

Produkt-Details

• Erscheint lt. Verlag: 21.7.2000
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-053709-X / 008053709X
• ISBN-13: 978-0-08-053709-2 / 9780080537092