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Smoothed Particle Hydrodynamics : A Meshfree Particle Method - M. B. Liu

Smoothed Particle Hydrodynamics

A Meshfree Particle Method

By: M. B. Liu, Gui-Rong Liu (Editor)

Hardcover

Published: 10th October 2003
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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.

"? One of the unique features of the book is its emphasis on the computer implementation and coding of SPH method."

Prefacep. vii
Introductionp. 1
Numerical Simulationp. 1
Role of Numerical Simulationp. 1
Solution Procedure of General Numerical Simulationsp. 2
Grid-based Methodsp. 5
Lagrangian Gridp. 7
Eulerian Gridp. 9
Combined Lagrangian and Eulerian Gridsp. 10
Limitations of the Grid-Based Methodsp. 12
Meshfree Methodsp. 13
Meshfree Particle Methods (MPMs)p. 18
Solution Strategy of MPMsp. 21
Particle Representationp. 22
Particle Approximationp. 24
Solution Procedure of MPMsp. 24
Smoothed Particle Hydrodynamics (SPH)p. 26
The SPH Methodp. 26
Briefing on the History of the SPH Methodp. 27
The SPH Method in This Bookp. 30
SPH Concept and Essential Formulationp. 33
Basic Ideas of SPHp. 33
Essential Formulation of SPHp. 35
Integral Representation of a Functionp. 35
Integral Representation of the Derivative of a Functionp. 38
Particle Approximationp. 40
Some Techniques in Deriving SPH Formulationsp. 44
Other Fundamental Issuesp. 46
Support and Influence Domainp. 46
Physical Influence Domainp. 51
Particle-in-Cell (PIC) Methodp. 52
Concluding Remarksp. 56
Constructing Smoothing Functionsp. 59
Introductionp. 59
Conditions for Constructing Smoothing Functionsp. 68
Approximation of a Field Functionp. 69
Approximation of the Derivatives of a Field Functionp. 71
Consistency of the Kernel Approximationp. 77
Consistency of the Particle Approximationp. 79
Constructing Smoothing Functionsp. 84
Constructing Smoothing Functions in Polynomial Formp. 84
Some Related Issuesp. 85
Examples of Constructing Smoothing Functionsp. 87
Dome-Shaped Quadratic Smoothing Functionp. 87
Quartic Smoothing Functionp. 89
Piecewise Cubic Smoothing Functionp. 90
Piecewise Quintic Smoothing Functionp. 91
A New Quartic Smoothing Functionp. 92
Numerical Testsp. 93
Shock Tube Problemp. 94
Two-Dimensional Heat Conductionp. 97
Concluding Remarksp. 101
SPH for General Dynamic Fluid Flowsp. 103
Introductionp. 104
Navier-Stokes Equations in Lagrangian Formp. 105
Finite Control Volume and Infinitesimal Fluid Cellp. 106
The Continuity Equationp. 109
The Momentum Equationp. 110
The Energy Equationp. 112
Navier-Stokes Equationsp. 113
SPH Formulations for Navier-Stokes Equationsp. 114
Particle Approximation of Densityp. 114
Particle Approximation of Momentump. 117
Particle Approximation of Energyp. 120
Numerical Aspects of SPH for Dynamic Fluid Flowsp. 125
Artificial Viscosityp. 125
Artificial Heatp. 127
Physical Viscosity Descriptionp. 128
Variable Smoothing Lengthp. 129
Symmetrization of Particle Interactionp. 130
Zero-Energy Modep. 132
Artificial Compressibilityp. 136
Boundary Treatmentp. 138
Time Integrationp. 141
Particle Interactionsp. 143
Nearest Neighboring Particle Searching (NNPS)p. 143
Pairwise Interactionp. 147
Numerical Examplesp. 149
Applications to Incompressible Flowsp. 149
Poiseuille Flowp. 149
Couette Flowp. 154
Shear Driven Cavity Problemp. 156
Applications to Free Surface Flowsp. 160
Water Splashp. 160
Water Dischargep. 160
Dam Collapsep. 161
Applications to Compressible Flowsp. 172
Gas Expansionp. 172
Concluding Remarksp. 176
Discontinuous SPH (DSPH)p. 177
Introductionp. 178
Corrective Smoothed Particle Method (CSPM)p. 180
One-Dimensional Casep. 180
Multi-Dimensional Casep. 183
DSPH Formulation for Simulating Discontinuous Phenomenap. 184
DSPH Formulationp. 184
Discontinuity Detectionp. 190
Numerical Performance Studyp. 191
Discontinuous Function Simulationp. 191
Simulation of Shock Wavesp. 195
Shock Discontinuity Simulationp. 195
Concluding Remarksp. 200
SPH for Simulating Explosionsp. 201
Introductionp. 202
HE Explosions and Governing Equationsp. 203
Explosion Processp. 203
HE Steady State Detonationp. 204
Governing Equationsp. 206
SPH Formulationsp. 208
Smoothing Lengthp. 210
Initial Distribution of Particlesp. 211
Updating of Smoothing Lengthp. 213
Optimization and Relaxation Procedurep. 214
Numerical Examplesp. 214
One-Dimensional TNT Slab Detonationp. 215
Two-Dimensional Explosive Gas Expansionp. 223
Application of SPH to Shaped Charge Simulationp. 229
Backgroundp. 229
Shaped Charge with a Conic Cavity and a Plane Ignitionp. 231
Shaped Charge with a Conic Cavity and a Point Ignitionp. 238
Shaped Charge with a Hemi-Elliptic Cavity and a Plane Ignitionp. 245
Effects of Charge Head Lengthp. 250
Concluding Remarksp. 252
SPH for Underwater Explosion Shock Simulationp. 255
Introductionp. 256
Underwater Explosions and Governing Equationsp. 258
Underwater Explosion Shock Physicsp. 258
Governing Equationsp. 259
SPH Formulationsp. 263
Interface Treatmentp. 264
Numerical Examplesp. 267
UNDEX of a Cylindrical TNT Chargep. 267
UNDEX of a Square TNT Chargep. 273
Comparison Study of the Real and Artificial HE Detonation Modelsp. 281
One-Dimensional TNT Slabp. 281
UNDEX Shock by a TNT Slab Chargep. 284
UNDEX Shock with a Spherical TNT Chargep. 286
Water Mitigation Simulationp. 288
Backgroundp. 288
Simulation Setupp. 290
Simulation Resultsp. 293
Explosion Shock Wave in Airp. 293
Contact Water Mitigationp. 295
Non-Contact Water Mitigationp. 300
Summaryp. 306
Concluding Remarksp. 306
SPH for Hydrodynamics with Material Strengthp. 309
Introductionp. 309
Hydrodynamics with Material Strengthp. 311
Governing Equationsp. 311
Constitutive Modelingp. 312
Equation of Statep. 313
Temperaturep. 314
Sound Speedp. 314
SPH Formulation for Hydrodynamics with Material Strengthp. 315
Tensile Instabilityp. 317
Adaptive Smoothed Particle Hydrodynamics (ASPH)p. 319
Why ASPHp. 319
Main Idea of ASPHp. 320
Applications to Hydrodynamics with Material Strengthp. 323
A Cylinder Impacting on a Rigid Surfacep. 324
HVI of a Cylinder on a Platep. 330
Concluding Remarksp. 339
Coupling SPH with Molecular Dynamics for Multiple Scale Simulationsp. 341
Introductionp. 341
Molecular Dynamicsp. 343
Fundamentals of Molecular Dynamicsp. 343
Classic Molecular Dynamicsp. 345
Classic MD Simulation Implementationp. 351
MD Simulation of the Poiseuille Flowp. 352
Coupling MD with FEM and FDMp. 354
Coupling SPH with MDp. 356
Model I: Dual Functioning (with Overlapping)p. 357
Model II: Force Briding (without Overlapping)p. 359
Numerical Testsp. 360
Concluding Remarksp. 364
Computer Implementation of SPH and a 3D SPH Codep. 365
General Procedure for Lagrangian Particle Simulationp. 366
SPH Code for Scalar Machinesp. 367
SPH Code for Parallel Machinesp. 368
Parallel Architectures and Parallel Computingp. 368
Parallel SPH Codep. 371
A 3D SPH Code for Solving the N-S Equationsp. 375
Main Features of the 3D SPH Codep. 376
Conventions for Naming Variables in FORTRANp. 377
Description of the SPH Codep. 378
Two Benchmark Problemsp. 385
List of the FORTRAN Source Filesp. 389
Bibliographyp. 423
Indexp. 445
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789812384560
ISBN-10: 9812384561
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 472
Published: 10th October 2003
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 23.93 x 15.9  x 2.87
Weight (kg): 0.83