 | Liu M.-B. Particle methods for multi-scale and multi-physics / by M.-B.Liu, G.-R.Liu. - London: Imperial College; Singapore; Hackensack: World Scientific Publishing, 2016. - xxi, 377 p.: ill., tab. - Bibliogr. at the end of the chapters. - Ind.: p.373-377.
- ISBN 978-981-4571-69-2
Шифр: (И/В19-L82) 02
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Preface ....................................................... vii
Acknowledgments ................................................
1 Introduction ............................................... 1
1.1 Computer modeling .......................................... 1
1.1.1 Computer modeling and its general solution
procedure ........................................... 1
1.1.2 Computer modeling, theory and experiment ............ 4
1.1.3 Verification and validation ......................... 5
1.2 Governing equations ........................................ 6
1.2.1 Eulerian and Lagrangian descriptions ................ 7
1.2.2 Control volume, surface and velocity divergence ..... 8
1.2.3 Navier-Stokes equations in Lagrangian frame ........ 10
1.3 Grid-based methods ........................................ 14
1.3.1 Lagrangian grid .................................... 16
1.3.2 Eulerian grid ...................................... 18
1.3.3 Combined Lagrangian and Eulerian grids ............. 20
1.3.4 Limitations of the grid-based methods .............. 20
1.4 Meshfree methods .......................................... 21
1.4.1 Types of methods ................................... 21
1.4.2 Applications ....................................... 23
1.4.3 Particle methods - a special class of meshfree
methods ............................................ 26
1.5 Solution strategy of particle methods ..................... 29
1.5.1 Particle representation ............................ 30
1.5.2 Particle approximation ............................. 31
1.5.3 Solution procedure ................................. 33
References ................................................ 34
2 Molecular Dynamics ........................................ 43
2.1 Introduction .............................................. 44
2.2 Classic Molecular Dynamics ................................ 46
2.2.1 Equations of motion ................................ 46
2.2.2 Force potential function ........................... 47
2.2.3 Time integration ................................... 50
2.2.4 Periodic boundary treatment ........................ 51
2.2.5 Classic MD simulation implementation ............... 52
2.2.6 MD simulation of Poiseuille flow ................... 54
2.3 Coupling MD with macro scale methods ...................... 56
2.3.1 An overview ........................................ 56
2.3.2 Coupling MD with FEM ............................... 58
2.3.3 Coupling MD with FDM ............................... 59
2.3.4 Coupling MD with SPH ............................... 60
2.4 Molecular dynamics simulation of peptide-CNT interaction .. 62
2.4.1 General overview of CNTs ........................... 62
2.4.2 General overview of proteins and peptides .......... 64
2.4.3 Setup of the MD simulation of peptide-CNT
interaction ........................................ 66
2.4.4 Results and discussions ............................ 69
2.5 Concluding remarks ........................................ 77
References ................................................ 78
3 Dissipative Particle Dynamics - Methodology ............... 83
3.1 Introduction .............................................. 84
3.2 Basic concepts of dissipative particle dynamics ........... 87
3.2.1 Coarse-graining .................................... 87
3.2.2 Governing equations ................................ 88
3.2.3 Time integration ................................... 91
3.2.4 Stress tensor ...................................... 92
3.2.5 Determination of coefficients ...................... 92
3.2.6 Computational procedure ............................ 94
3.3 Numerical aspects ......................................... 96
3.3.1 Assessment of dynamic properties ................... 96
3.3.2 Solid boundary treatment ........................... 99
3.3.3 Conservative interaction potential ................ 102
3.3.4 Spring-bead chain models .......................... 109
3.4 Validation of the DPD method ............................. 110
3.4.1 Binary mixture .................................... 110
3.4.2 Poiseuille flow ................................... 113
3.4.3 Fully saturated flow through porous media ......... 116
3.5 Concluding remarks ....................................... 120
References ............................................... 122
4 Dissipative Particle Dynamics - Applications ............. 127
4.1 Introduction ............................................. 127
4.2 Micro drop dynamics ...................................... 129
4.2.1 Formation of drop with co-existing liquid-vapor ... 131
4.2.2 Large-amplitude oscillation of a liquid drop ...... 138
4.2.3 Controlled drug delivery .......................... 139
4.3 Multiphase flows in pore-scale fracture network and
porous media ............................................. 141
4.3.1 Multiphase flows in micro channel and fractures ... 143
4.3.2 Multiphase flows in porous media .................. 152
4.4 Movement and suspension of macromolecules in micro
channels ................................................. 159
4.4.1 Straight micro channel ............................ 163
4.4.2 Contracted micro channel .......................... 166
4.4.3 Inclined micro channel ............................ 167
4.4.4 Grooved micro-channel ............................. 169
4.5 Movement and deformation of single cells ................. 178
4.6 Concluding remarks ....................................... 183
References ............................................... 184
5 Smoothed Particle Hydrodynamics - Methodology ............ 191
5.1 History and development .................................. 192
5.2 Basic concepts of SPH approximation ...................... 196
5.2.1 Kernel approximation of a function ................ 196
5.2.2 Kernel approximation of derivatives ............... 198
5.2.3 Particle approximation ............................ 201
5.2.4 Techniques for deriving SPH formulations .......... 203
5.2.5 SPH formulations for the Navier-Stokes (N-S)
equations ......................................... 205
5.3 SPH smoothing function ................................... 207
5.3.1 Review on commonly used smoothing functions ....... 207
5.3.2 Generalizing constructing conditions .............. 212
5.3.3 Constructing SPH smoothing functions .............. 214
5.4 Numerical aspects of SPH ................................. 217
5.4.1 Artificial viscosity .............................. 217
5.4.2 Artificial heat ................................... 219
5.4.3 Smoothing length .................................. 220
5.4.4 Symmetrization of particle interaction ............ 221
5.4.5 Tensile instability ............................... 222
5.5 Consistency of the SPH method ............................ 224
5.5.1 Consistency in kernel approximation (kernel
consistency) ...................................... 224
5.5.2 Consistency in particle approximation (particle
consistency) ...................................... 226
5.5.3 Review on approaches for restoring consistency .... 228
5.5.4 A general approach to restore particle
consistency ....................................... 231
5.5.5 Finite particle method ............................ 233
5.5.6 A comparative study of particle consistency ....... 239
5.5.7 Consistency vs. stability ......................... 251
5.6 Concluding remarks ....................................... 252
References ............................................... 253
6 Smoothed Particle Hydrodynamics - Applications ........... 261
6.1 Introduction ............................................. 262
6.1.1 Review on SPH applications ........................ 262
6.1.2 Applications to hydrodynamics and ocean
engineering ....................................... 264
6.2 Governing equations ...................................... 266
6.2.1 Governing equation for viscous incompressible
fluid flow ........................................ 266
6.2.2 Governing equation for moving rigid body .......... 267
6.2.3 SPH equations of motion ........................... 268
6.2.4 Density and kernel gradient correction ............ 269
6.3 Modeling incompressible flows in SPH ..................... 272
6.3.1 Weakly compressible SPH (WCSPH) model ............. 273
6.3.2 Incompressible SPH (ISPH) algorithm ............... 275
6.3.3 Comparisons of WCSPH and ISPH ..................... 278
6.4 Free surface flows ....................................... 288
6.4.1 Dam breaking against a vertical wall .............. 289
6.4.2 Dam breaking against a sharp-edged obstacle ....... 294
6.4.3 The movement of an elliptical cylinder near free
surface ........................................... 294
6.5 Liquid sloshing .......................................... 298
6.5.1 Liquid sloshing under horizontal excitation ....... 300
6.5.2 Liquid sloshing with a middle baffle .............. 302
6.5.3 Liquid sloshing due to the pitch motion of
a rectangular tank ................................ 304
6.5.4 Ballast water ..................................... 308
6.6 Water entry and exit ..................................... 312
6.6.1 Water exit of a cylinder .......................... 312
6.6.2 Sinking of a submerged cylinder ................... 315
6.6.3 Free falling of a cylinder ........................ 317
6.6.4 Underwater launch ................................. 319
6.7 Oil spill and boom movement .............................. 322
6.7.1 Effects of oil type ............................... 325
6.7.2 Effects of boom velocity .......................... 326
6.7.3 Effects of skirt angle ............................ 326
6.7.4 Effects of waves .................................. 327
6.8 Hydro-elasticity ......................................... 328
6.8.1 Head-on collision of two rubber rings ............. 329
6.8.2 Dam break with an elastic gate .................... 331
6.8.3 Water impact onto a forefront elastic plate ....... 333
6.9 Concluding remarks ....................................... 335
References ............................................... 337
7 Three Typical Particle Methods ........................... 353
7.1 Particle-in-cell method .................................. 354
7.1.1 History and development ........................... 354
7.1.2 Basic concept ..................................... 354
7.1.3 Implementation procedure .......................... 356
7.1.4 Comparison of SPH and PIC ......................... 357
7.2 Material point method .................................... 357
7.2.1 History and development ........................... 357
7.2.2 Basic concept ..................................... 358
7.2.3 Implementation procedure .......................... 361
7.2.4 Comparison of SPH and MPM ......................... 362
7.3 Moving-particle semi-implicit method ..................... 363
7.3.1 History and development ........................... 363
7.3.2 Basic concept ..................................... 364
7.3.3 Implementation procedure .......................... 367
7.3.4 Comparison of SPH and MPS ......................... 368
7.4 Concluding remarks ....................................... 369
References ............................................... 370
Index ......................................................... 373
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