Smoothed particle hydrodynamics : a meshfree particle method

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, making this a friendly book for readers and SPH users.

Preface	p. vii
1 Introduction	p. 1
1.1 Numerical Simulation	p. 1
1.1.1 Role of Numerical Simulation	p. 1
1.1.2 Solution Procedure of General Numerical Simulations	p. 2
1.2 Grid-based Methods	p. 5
1.2.1 Lagrangian Grid	p. 7
1.2.2 Eulerian Grid	p. 9
1.2.3 Combined Lagrangian and Eulerian Grids	p. 10
1.2.4 Limitations of the Grid-Based Methods	p. 12
1.3 Meshfree Methods	p. 13
1.4 Meshfree Particle Methods (MPMs)	p. 18
1.5 Solution Strategy of MPMs	p. 21
1.5.1 Particle Representation	p. 22
1.5.2 Particle Approximation	p. 24
1.5.3 Solution Procedure of MPMs	p. 24
1.6 Smoothed Particle Hydrodynamics (SPH)	p. 26
1.6.1 The SPH Method	p. 26
1.6.2 Briefing on the History of the SPH Method	p. 27
1.6.3 The SPH Method in This Book	p. 30
2 SPH Concept and Essential Formulation	p. 33
2.1 Basic Ideas of SPH	p. 33
2.2 Essential Formulation of SPH	p. 35
2.2.1 Integral Representation of a Function	p. 35
2.2.2 Integral Representation of the Derivative of a Function	p. 38
2.2.3 Particle Approximation	p. 40
2.2.4 Some Techniques in Deriving SPH Formulations	p. 44
2.3 Other Fundamental Issues	p. 46
2.3.1 Support and Influence Domain	p. 46
2.3.2 Physical Influence Domain	p. 51
2.3.3 Particle-in-Cell (PIC) Method	p. 52
2.4 Concluding Remarks	p. 56
3 Constructing Smoothing Functions	p. 59
3.1 Introduction	p. 59
3.2 Conditions for Constructing Smoothing Functions	p. 68
3.2.1 Approximation of a Field Function	p. 69
3.2.2 Approximation of the Derivatives of a Field Function	p. 71
3.2.3 Consistency of the Kernel Approximation	p. 77
3.2.4 Consistency of the Particle Approximation	p. 79
3.3 Constructing Smoothing Functions	p. 84
3.3.1 Constructing Smoothing Functions in Polynomial Form	p. 84
3.3.2 Some Related Issues	p. 85
3.3.3 Examples of Constructing Smoothing Functions	p. 87
Example 3.1 Dome-Shaped Quadratic Smoothing Function	p. 87
Example 3.2 Quartic Smoothing Function	p. 89
Example 3.3 Piecewise Cubic Smoothing Function	p. 90
Example 3.4 Piecewise Quintic Smoothing Function	p. 91
Example 3.5 A New Quartic Smoothing Function	p. 92
3.4 Numerical Tests	p. 93
Example 3.6 Shock Tube Problem	p. 94
Example 3.7 Two-Dimensional Heat Conduction	p. 97
3.5 Concluding Remarks	p. 101
4 SPH for General Dynamic Fluid Flows	p. 103
4.1 Introduction	p. 104
4.2 Navier-Stokes Equations in Lagrangian Form	p. 105
4.2.1 Finite Control Volume and Infinitesimal Fluid Cell	p. 106
4.2.2 The Continuity Equation	p. 109
4.2.3 The Momentum Equation	p. 110
4.2.4 The Energy Equation	p. 112
4.2.5 Navier-Stokes Equations	p. 113
4.3 SPH Formulations for Navier-Stokes Equations	p. 114
4.3.1 Particle Approximation of Density	p. 114
4.3.2 Particle Approximation of Momentum	p. 117
4.3.3 Particle Approximation of Energy	p. 120
4.4 Numerical Aspects of SPH for Dynamic Fluid Flows	p. 125
4.4.1 Artificial Viscosity	p. 125
4.4.2 Artificial Heat	p. 127
4.4.3 Physical Viscosity Description	p. 128
4.4.4 Variable Smoothing Length	p. 129
4.4.5 Symmetrization of Particle Interaction	p. 130
4.4.6 Zero-Energy Mode	p. 132
4.4.7 Artificial Compressibility	p. 136
4.4.8 Boundary Treatment	p. 138
4.4.9 Time Integration	p. 141
4.5 Particle Interactions	p. 143
4.5.1 Nearest Neighboring Particle Searching (NNPS)	p. 143
4.5.2 Pairwise Interaction	p. 147
4.6 Numerical Examples	p. 149
4.6.1 Applications to Incompressible Flows	p. 149
Example 4.1 Poiseuille Flow	p. 149
Example 4.2 Couette Flow	p. 154
Example 4.3 Shear Driven Cavity Problem	p. 156
4.6.2 Applications to Free Surface Flows	p. 160
Example 4.4 Water Splash	p. 160
Example 4.5 Water Discharge	p. 160
Example 4.6 Dam Collapse	p. 161
4.6.3 Applications to Compressible Flows	p. 172
Example 4.7 Gas Expansion	p. 172
4.7 Concluding Remarks	p. 176
5 Discontinuous SPH (DSPH)	p. 177
5.1 Introduction	p. 178
5.2 Corrective Smoothed Particle Method (CSPM)	p. 180
5.2.1 One-Dimensional Case	p. 180
5.2.2 Multi-Dimensional Case	p. 183
5.3 DSPH Formulation for Simulating Discontinuous Phenomena	p. 184
5.3.1 DSPH Formulation	p. 184
5.3.2 Discontinuity Detection	p. 190
5.4 Numerical Performance Study	p. 191
Example 5.1 Discontinuous Function Simulation	p. 191
5.5 Simulation of Shock Waves	p. 195
Example 5.2 Shock Discontinuity Simulation	p. 195
5.6 Concluding Remarks	p. 200
6 SPH for Simulating Explosions	p. 201
6.1 Introduction	p. 202
6.2 HE Explosions and Governing Equations	p. 203
6.2.1 Explosion Process	p. 203
6.2.2 HE Steady State Detonation	p. 204
6.2.3 Governing Equations	p. 206
6.3 SPH Formulations	p. 208
6.4 Smoothing Length	p. 210
6.4.1 Initial Distribution of Particles	p. 211
6.4.2 Updating of Smoothing Length	p. 213
6.4.3 Optimization and Relaxation Procedure	p. 214
6.5 Numerical Examples	p. 214
Example 6.1 One-Dimensional TNT Slab Detonation	p. 215
Example 6.2 Two-Dimensional Explosive Gas Expansion	p. 223
6.6 Application of SPH to Shaped Charge Simulation	p. 229
6.6.1 Background	p. 229
Example 6.3 Shaped Charge with a Conic Cavity and a Plane Ignition	p. 231
Example 6.4 Shaped Charge with a Conic Cavity and a Point Ignition	p. 238
Example 6.5 Shaped Charge with a Hemi-Elliptic Cavity and a Plane Ignition	p. 245
Example 6.6 Effects of Charge Head Length	p. 250
6.7 Concluding Remarks	p. 252
7 SPH for Underwater Explosion Shock Simulation	p. 255
7.1 Introduction	p. 256
7.2 Underwater Explosions and Governing Equations	p. 258
7.2.1 Underwater Explosion Shock Physics	p. 258
7.2.2 Governing Equations	p. 259
7.3 SPH Formulations	p. 263
7.4 Interface Treatment	p. 264
7.5 Numerical Examples	p. 267
Example 7.1 UNDEX of a Cylindrical TNT Charge	p. 267
Example 7.2 UNDEX of a Square TNT Charge	p. 273
7.6 Comparison Study of the Real and Artificial HE Detonation Models	p. 281
Example 7.3 One-Dimensional TNT Slab	p. 281
Example 7.4 UNDEX Shock by a TNT Slab Charge	p. 284
Example 7.5 UNDEX Shock with a Spherical TNT Charge	p. 286
7.7 Water Mitigation Simulation	p. 288
7.7.1 Background	p. 288
7.7.2 Simulation Setup	p. 290
7.7.3 Simulation Results	p. 293
Example 7.6 Explosion Shock Wave in Air	p. 293
Example 7.7 Contact Water Mitigation	p. 295
Example 7.8 Non-Contact Water Mitigation	p. 300
7.7.4 Summary	p. 306
7.8 Concluding Remarks	p. 306
8 SPH for Hydrodynamics with Material Strength	p. 309
8.1 Introduction	p. 309
8.2 Hydrodynamics with Material Strength	p. 311
8.2.1 Governing Equations	p. 311
8.2.2 Constitutive Modeling	p. 312
8.2.3 Equation of State	p. 313
8.2.4 Temperature	p. 314
8.2.5 Sound Speed	p. 314
8.3 SPH Formulation for Hydrodynamics with Material Strength	p. 315
8.4 Tensile Instability	p. 317
8.5 Adaptive Smoothed Particle Hydrodynamics (ASPH)	p. 319
8.5.1 Why ASPH	p. 319
8.5.2 Main Idea of ASPH	p. 320
8.6 Applications to Hydrodynamics with Material Strength	p. 323
Example 8.1 A Cylinder Impacting on a Rigid Surface	p. 324
Example 8.2 HVI of a Cylinder on a Plate	p. 330
8.7 Concluding Remarks	p. 339
9 Coupling SPH with Molecular Dynamics for Multiple Scale Simulations	p. 341
9.1 Introduction	p. 341
9.2 Molecular Dynamics	p. 343
9.2.1 Fundamentals of Molecular Dynamics	p. 343
9.2.2 Classic Molecular Dynamics	p. 345
9.2.3 Classic MD Simulation Implementation	p. 351
9.2.4 MD Simulation of the Poiseuille Flow	p. 352
9.3 Coupling MD with FEM and FDM	p. 354
9.4 Coupling SPH with MD	p. 356
9.4.1 Model I: Dual Functioning (with Overlapping)	p. 357
9.4.2 Model II: Force Briding (without Overlapping)	p. 359
9.4.3 Numerical Tests	p. 360
9.5 Concluding Remarks	p. 364
10 Computer Implementation of SPH and a 3D SPH Code	p. 365
10.1 General Procedure for Lagrangian Particle Simulation	p. 366
10.2 SPH Code for Scalar Machines	p. 367
10.3 SPH Code for Parallel Machines	p. 368
10.3.1 Parallel Architectures and Parallel Computing	p. 368
10.3.2 Parallel SPH Code	p. 371
10.4 A 3D SPH Code for Solving the N-S Equations	p. 375
10.4.1 Main Features of the 3D SPH Code	p. 376
10.4.2 Conventions for Naming Variables in FORTRAN	p. 377
10.4.3 Description of the SPH Code	p. 378
10.4.4 Two Benchmark Problems	p. 385
10.4.5 List of the FORTRAN Source Files	p. 389
Bibliography	p. 423
Index	p. 445

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