Smoothed Particle Hydrodynamics : A Meshfree Particle Method

by Liu, G. R.; Liu, M. B.

• ISBN13: 9789812384560
• ISBN10: 9812384561
• Format: Hardcover
• Copyright: 2003-12-01
• Publisher: World Scientific Pub Co Inc

Summary

This is the first-ever book on smoothed particle hydrodynamics (SPH) and its variations, covering the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. It contains many appealing and practical examples, including free surface flows, high explosive detonation and explosion, underwater explosion and water mitigation of explosive shocks, high velocity impact and penetration, and multiple scale simulations coupled with the molecular dynamics method. An SPH source code is provided and coupling of SPH and molecular dynamics is discussed for multiscale simulation, making this a friendly book for readers and SPH users.

Table of Contents

Preface	p. vii
Introduction	p. 1
Numerical Simulation	p. 1
Role of Numerical Simulation	p. 1
Solution Procedure of General Numerical Simulations	p. 2
Grid-based Methods	p. 5
Lagrangian Grid	p. 7
Eulerian Grid	p. 9
Combined Lagrangian and Eulerian Grids	p. 10
Limitations of the Grid-Based Methods	p. 12
Meshfree Methods	p. 13
Meshfree Particle Methods (MPMs)	p. 18
Solution Strategy of MPMs	p. 21
Particle Representation	p. 22
Particle Approximation	p. 24
Solution Procedure of MPMs	p. 24
Smoothed Particle Hydrodynamics (SPH)	p. 26
The SPH Method	p. 26
Briefing on the History of the SPH Method	p. 27
The SPH Method in This Book	p. 30
SPH Concept and Essential Formulation	p. 33
Basic Ideas of SPH	p. 33
Essential Formulation of SPH	p. 35
Integral Representation of a Function	p. 35
Integral Representation of the Derivative of a Function	p. 38
Particle Approximation	p. 40
Some Techniques in Deriving SPH Formulations	p. 44
Other Fundamental Issues	p. 46
Support and Influence Domain	p. 46
Physical Influence Domain	p. 51
Particle-in-Cell (PIC) Method	p. 52
Concluding Remarks	p. 56
Constructing Smoothing Functions	p. 59
Introduction	p. 59
Conditions for Constructing Smoothing Functions	p. 68
Approximation of a Field Function	p. 69
Approximation of the Derivatives of a Field Function	p. 71
Consistency of the Kernel Approximation	p. 77
Consistency of the Particle Approximation	p. 79
Constructing Smoothing Functions	p. 84
Constructing Smoothing Functions in Polynomial Form	p. 84
Some Related Issues	p. 85
Examples of Constructing Smoothing Functions	p. 87
Dome-Shaped Quadratic Smoothing Function	p. 87
Quartic Smoothing Function	p. 89
Piecewise Cubic Smoothing Function	p. 90
Piecewise Quintic Smoothing Function	p. 91
A New Quartic Smoothing Function	p. 92
Numerical Tests	p. 93
Shock Tube Problem	p. 94
Two-Dimensional Heat Conduction	p. 97
Concluding Remarks	p. 101
SPH for General Dynamic Fluid Flows	p. 103
Introduction	p. 104
Navier-Stokes Equations in Lagrangian Form	p. 105
Finite Control Volume and Infinitesimal Fluid Cell	p. 106
The Continuity Equation	p. 109
The Momentum Equation	p. 110
The Energy Equation	p. 112
Navier-Stokes Equations	p. 113
SPH Formulations for Navier-Stokes Equations	p. 114
Particle Approximation of Density	p. 114
Particle Approximation of Momentum	p. 117
Particle Approximation of Energy	p. 120
Numerical Aspects of SPH for Dynamic Fluid Flows	p. 125
Artificial Viscosity	p. 125
Artificial Heat	p. 127
Physical Viscosity Description	p. 128
Variable Smoothing Length	p. 129
Symmetrization of Particle Interaction	p. 130
Zero-Energy Mode	p. 132
Artificial Compressibility	p. 136
Boundary Treatment	p. 138
Time Integration	p. 141
Particle Interactions	p. 143
Nearest Neighboring Particle Searching (NNPS)	p. 143
Pairwise Interaction	p. 147
Numerical Examples	p. 149
Applications to Incompressible Flows	p. 149
Poiseuille Flow	p. 149
Couette Flow	p. 154
Shear Driven Cavity Problem	p. 156
Applications to Free Surface Flows	p. 160
Water Splash	p. 160
Water Discharge	p. 160
Dam Collapse	p. 161
Applications to Compressible Flows	p. 172
Gas Expansion	p. 172
Concluding Remarks	p. 176
Discontinuous SPH (DSPH)	p. 177
Introduction	p. 178
Corrective Smoothed Particle Method (CSPM)	p. 180
One-Dimensional Case	p. 180
Multi-Dimensional Case	p. 183
DSPH Formulation for Simulating Discontinuous Phenomena	p. 184
DSPH Formulation	p. 184
Discontinuity Detection	p. 190
Numerical Performance Study	p. 191
Discontinuous Function Simulation	p. 191
Simulation of Shock Waves	p. 195
Shock Discontinuity Simulation	p. 195
Concluding Remarks	p. 200
SPH for Simulating Explosions	p. 201
Introduction	p. 202
HE Explosions and Governing Equations	p. 203
Explosion Process	p. 203
HE Steady State Detonation	p. 204
Governing Equations	p. 206
SPH Formulations	p. 208
Smoothing Length	p. 210
Initial Distribution of Particles	p. 211
Updating of Smoothing Length	p. 213
Optimization and Relaxation Procedure	p. 214
Numerical Examples	p. 214
One-Dimensional TNT Slab Detonation	p. 215
Two-Dimensional Explosive Gas Expansion	p. 223
Application of SPH to Shaped Charge Simulation	p. 229
Background	p. 229
Shaped Charge with a Conic Cavity and a Plane Ignition	p. 231
Shaped Charge with a Conic Cavity and a Point Ignition	p. 238
Shaped Charge with a Hemi-Elliptic Cavity and a Plane Ignition	p. 245
Effects of Charge Head Length	p. 250
Concluding Remarks	p. 252
SPH for Underwater Explosion Shock Simulation	p. 255
Introduction	p. 256
Underwater Explosions and Governing Equations	p. 258
Underwater Explosion Shock Physics	p. 258
Governing Equations	p. 259
SPH Formulations	p. 263
Interface Treatment	p. 264
Numerical Examples	p. 267
UNDEX of a Cylindrical TNT Charge	p. 267
UNDEX of a Square TNT Charge	p. 273
Comparison Study of the Real and Artificial HE Detonation Models	p. 281
One-Dimensional TNT Slab	p. 281
UNDEX Shock by a TNT Slab Charge	p. 284
UNDEX Shock with a Spherical TNT Charge	p. 286
Water Mitigation Simulation	p. 288
Background	p. 288
Simulation Setup	p. 290
Simulation Results	p. 293
Explosion Shock Wave in Air	p. 293
Contact Water Mitigation	p. 295
Non-Contact Water Mitigation	p. 300
Summary	p. 306
Concluding Remarks	p. 306
SPH for Hydrodynamics with Material Strength	p. 309
Introduction	p. 309
Hydrodynamics with Material Strength	p. 311
Governing Equations	p. 311
Constitutive Modeling	p. 312
Equation of State	p. 313
Temperature	p. 314
Sound Speed	p. 314
SPH Formulation for Hydrodynamics with Material Strength	p. 315
Tensile Instability	p. 317
Adaptive Smoothed Particle Hydrodynamics (ASPH)	p. 319
Why ASPH	p. 319
Main Idea of ASPH	p. 320
Applications to Hydrodynamics with Material Strength	p. 323
A Cylinder Impacting on a Rigid Surface	p. 324
HVI of a Cylinder on a Plate	p. 330
Concluding Remarks	p. 339
Coupling SPH with Molecular Dynamics for Multiple Scale Simulations	p. 341
Introduction	p. 341
Molecular Dynamics	p. 343
Fundamentals of Molecular Dynamics	p. 343
Classic Molecular Dynamics	p. 345
Classic MD Simulation Implementation	p. 351
MD Simulation of the Poiseuille Flow	p. 352
Coupling MD with FEM and FDM	p. 354
Coupling SPH with MD	p. 356
Model I: Dual Functioning (with Overlapping)	p. 357
Model II: Force Briding (without Overlapping)	p. 359
Numerical Tests	p. 360
Concluding Remarks	p. 364
Computer Implementation of SPH and a 3D SPH Code	p. 365
General Procedure for Lagrangian Particle Simulation	p. 366
SPH Code for Scalar Machines	p. 367
SPH Code for Parallel Machines	p. 368
Parallel Architectures and Parallel Computing	p. 368
Parallel SPH Code	p. 371
A 3D SPH Code for Solving the N-S Equations	p. 375
Main Features of the 3D SPH Code	p. 376
Conventions for Naming Variables in FORTRAN	p. 377
Description of the SPH Code	p. 378
Two Benchmark Problems	p. 385
List of the FORTRAN Source Files	p. 389
Bibliography	p. 423
Index	p. 445
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