Preface -- The Authors -- Contents -- Chapter 1 Introduction -- 1.1 Numerical simulation -- 1.1.1 Role of numerical simulation -- 1.1.2 Solution procedure of general numerical simulations -- 1.2 Grid-based methods -- 1.2.1 Lagrangian grid -- 1.2.2 Eulerian grid -- 1.2.3 Combined Lagrangian and Eulerian grids -- 1.2.4 Limitations of the grid-based methods -- 1.3 Meshfree methods -- 1.4 Meshfree particle methods (MPMs) -- 1.5 Solution strategy of MPMs -- 1.5.1 Particle representation -- 1.5.2 Particle approximation -- 1.5.3 Solution procedure of MPMs -- 1.6 Smoothed particle hydrodynamics (SPH) -- 1.6.1 The SPH method -- 1.6.2 Briefing on the history of the SPH method -- 1.6.3 The SPH method in this book -- Chapter 2 SPH Concept and Essential Formulation -- 2.1 Basic ideas of SPH -- 2.2 Essential formulation of SPH -- 2.2.1 Integral representation of a function -- 2.2.2 Integral representation of the derivative of a function -- 2.2.3 Particle approximation -- 2.2.4 Some techniques in deriving SPH formulations -- 2.3 Other fundamental issues -- 2.3.1 Support and influence domain -- 2.3.2 Physical influence domain -- 2.3.3 Particle-in-Cell (PIC) method -- 2.4 Concluding remarks -- Chapter 3 Construction of Smoothing Functions -- 3.1 Introduction -- 3.2 Conditions for constructing smoothing functions -- 3.2.1 Approximation of a field function -- 3.2.2 Approximation of the derivatives of a field function -- 3.2.3 Consistency of the kernel approximation -- 3.2.4 Consistency of the particle approximation -- 3.3 Constructing smoothing functions -- 3.3.1 Constructing smoothing functions in polynomial form -- 3.3.2 Some related issues -- 3.3.3 Examples of constructing smoothing functions -- 3.4 Numerical tests -- 3.5 Concluding remarks -- Chapter 4 SPH for General Dynamic Fluid Flows -- 4.1 Introduction -- 4.2 Navier-Stokes equations in Lagrangian form.

4.2.1 Finite control volume and infinitesimal fluid cell -- 4.2.2 The continuity equation -- 4.2.3 The momentum equation -- 4.2.4 The energy equation -- 4.2.5 Navier-Stokes equations -- 4.3 SPH formulations for Navier-Stokes equations -- 4.3.1 Particle approximation of density -- 4.3.2 Particle approximation of momentum -- 4.3.3 Particle approximation of energy -- 4.4 Numerical aspects of SPH for dynamic fluid flows -- 4.4.1 Artificial viscosity -- 4.4.2 Artificial heat -- 4.4.3 Physical viscosity description -- 4.4.4 Variable smoothing length -- 4.4.5 Symmetrization of particle interaction -- 4.4.6 Zero-energy mode -- 4.4.7 Artificial compressibility -- 4.4.8 Boundary treatment -- 4.4.9 Time integration -- 4.5 Particle interactions -- 4.5.1 Nearest neighboring particle searching (NNPS) -- 4.5.2 Pairwise interaction -- 4.6 Numerical examples -- 4.6.1 Applications to incompressible flows -- 4.6.2 Applications to free surface flows -- 4.6.3 Applications to compressible flows -- 4.7 Concluding remarks -- Chapter 5 Discontinuous SPH (DSPH) -- 5.1 Introduction -- 5.2 Corrective smoothed particle method (CSPM) -- 5.2.1 One-dimensional case -- 5.2.2 Multi-dimensional case -- 5.3 DSPH formulation for simulating discontinuous phenomena -- 5.3.1 DSPH formulation -- 5.3.2 Discontinuity detection -- 5.4 Numerical performance study -- 5.5 Simulation of shock waves -- 5.6 Concluding remarks -- Chapter 6 SPH for Simulating Explosions -- 6.1 Introduction -- 6.2 HE explosions and governing equations -- 6.2.1 Explosion process -- 6.2.2 HE steady state detonation -- 6.2.3 Governing equations -- 6.3 SPH formulations -- 6.4 Smoothing length -- 6.4.1 Initial distribution of particles -- 6.4.2 Updating of smoothing length -- 6.4.3 Optimization and relaxation procedure -- 6.5 Numerical examples -- 6.6 Application of SPH to shaped charge simulation -- 6.6.1 Background.

6.7 Concluding remarks -- Chapter 7 SPH for Underwater Explosion Shock Simulation -- 7.1 Introduction -- 7.2 Underwater explosions and governing equations -- 7.2.1 Underwater explosion shock physics -- 7.2.2 Governing equations -- 7.3 SPH formulations -- 7.4 Interface treatment -- 7.5 Numerical examples -- 7.6 Comparison study of the real and artificial HE detonation models -- 7.7 Water mitigation simulation -- 7.7.1 Background -- 7.7.2 Simulation setup -- 7.7.3 Simulation results -- 7.7.4 Summary -- 7.8 Concluding remarks -- Chapter 8 SPH for Hydrodynamics with Material Strength -- 8.1 Introduction -- 8.2 Hydrodynamics with material strength -- 8.2.1 Governing equations -- 8.2.2 Constitutive modeling -- 8.2.3 Equation of state -- 8.2.4 Temperature -- 8.2.5 Sound speed -- 8.3 SPH formulation for hydrodynamics with material strength -- 8.4 Tensile instability -- 8.5 Adaptive smoothed particle hydrodynamics (ASPH) -- 8.5.1 Why ASPH -- 8.5.2 Main idea of ASPH -- 8.6 Applications to hydrodynamics with material strength -- 8.7 Concluding remarks -- Chapter 9 Coupling SPH with Molecular Dynamics for Multiple Scale Simulations -- 9.1 Introduction -- 9.2 Molecular dynamics -- 9.2.1 Fundamentals of molecular dynamics -- 9.2.2 Classic Molecular Dynamics -- 9.2.3 Classic MD simulation implementation -- 9.2.4 MD simulation of the Poiseuille flow -- 9.3 Coupling MD with FEM and FDM -- 9.4 Coupling SPH with MD -- 9.4.1 Model I: Dual functioning (with overlapping) -- 9.4.2 Model II: Force bridging (without overlapping) -- 9.4.3 Numerical tests -- 9.5 Concluding remarks -- Chapter 10 Computer Implementation of SPH and a 3D SPH Code -- 10.1 General procedure for Lagrangian particle simulation -- 10.2 SPH code for scalar machines -- 10.3 SPH code for parallel machines -- 10.3.1 Parallel architectures and parallel computing -- 10.3.2 Parallel SPH code.

10.4 A 3D SPH code for solving the N-S equations -- 10.4.1 Main features of the 3D SPH code -- 10.4.2 Conventions for naming variables in FORTRAN -- 10.4.3 Description of the SPH code -- 10.4.4 Two benchmark problems -- 10.4.5 List of the FORTRAN source files -- Bibliography -- Index.