SPH方法最经典英文教材

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