Smoothed Particle Hydrodynamics

The following sections are included:

• Preface

• Contents

The following sections are included:

• Numerical simulation
  • Role of numerical simulation
  • Solution procedure of general numerical simulations

• Grid-based methods
  • Lagrangian grid
  • Eulerian grid
  • Combined Lagrangian and Eulerian grids
  • Limitations of the grid-based methods

• Meshfree methods

• Meshfree particle methods (MPMs)

• Solution strategy of MPMs
  • Particle representation
  • Particle approximation
  • Solution procedure of MPMs

• Smoothed particle hydrodynamics (SPH)
  • The SPH method
  • Briefing on the history of the SPH method
  • The SPH method in this book

The following sections are included:

• Basic ideas of SPH

• Essential formulation of SPH
  • Integral representation of a function
  • Integral representation of the derivative of a function
  • Particle approximation
  • Some techniques in deriving SPH formulations

• Other fundamental issues
  • Support and influence domain
  • Physical influence domain
  • Particle-in-Cell (PIC) method

• Concluding remarks

The following sections are included:

• Introduction

• Conditions for constructing smoothing functions
  • Approximation of a field function
  • Approximation of the derivatives of a field function
  • Consistency of the kernel approximation
  • Consistency of the particle approximation

• Constructing smoothing functions
  • Constructing smoothing functions in polynomial form
  • Some related issues
  • Examples of constructing smoothing functions

• Numerical tests

• Concluding remarks

The following sections are included:

• Introduction

• Navier-Stokes equations in Lagrangian form
  • Finite control volume and infinitesimal fluid cell
  • The continuity equation
  • The momentum equation
  • The energy equation
  • Navier-Stokes equations

• SPH formulations for Navier-Stokes equations
  • Particle approximation of density
  • Particle approximation of momentum
  • Particle approximation of energy

• Numerical aspects of SPH for dynamic fluid flows
  • Artificial viscosity
  • Artificial heat
  • Physical viscosity description
  • Variable smoothing length
  • Symmetrization of particle interaction
  • Zero-energy mode
  • Artificial compressibility
  • Boundary treatment
  • Time integration

• Particle interactions
  • Nearest neighboring particle searching (NNPS)
  • Pairwise interaction

• Numerical examples
  • Applications to incompressible flows
  • Applications to free surface flows
  • Applications to compressible flows

• Concluding remarks

The following sections are included:

• Introduction

• Corrective smoothed particle method (CSPM)
  • One-dimensional case
  • Multi-dimensional case

• DSPH formulation for simulating discontinuous phenomena
  • DSPH formulation
  • Discontinuity detection

• Numerical performance study

• Simulation of shock waves

• Concluding remarks

The following sections are included:

• Introduction

• HE explosions and governing equations
  • Explosion process
  • HE steady state detonation
  • Governing equations

• SPH formulations

• Smoothing length
  • Initial distribution of particles
  • Updating of smoothing length
  • Optimization and relaxation procedure

• Numerical examples

• Application of SPH to shaped charge simulation
  • Background

• Concluding remarks

The following sections are included:

• Introduction

• Underwater explosions and governing equations
  • Underwater explosion shock physics
  • Governing equations

• SPH formulations

• Interface treatment

• Numerical examples

• Comparison study of the real and artificial HE detonation models

• Water mitigation simulation
  • Background
  • Simulation setup
  • Simulation results
  • Summary

• Concluding remarks

The following sections are included:

• Introduction

• Hydrodynamics with material strength
  • Governing equations
  • Constitutive modeling
  • Equation of state
  • Temperature
  • Sound speed

• SPH formulation for hydrodynamics with material strength

• Tensile instability

• Adaptive smoothed particle hydrodynamics (ASPH)
  • Why ASPH
  • Main idea of ASPH

• Applications to hydrodynamics with material strength

• Concluding remarks

The following sections are included:

• Introduction

• Molecular dynamics
  • Fundamentals of molecular dynamics
  • Classic Molecular Dynamics
  • Classic MD simulation implementation
  • MD simulation of the Poiseuille flow

• Coupling MD with FEM and FDM

• Coupling SPH with MD
  • Model I: Dual functioning (with overlapping)
  • Model II: Force bridging (without overlapping)
  • Numerical tests

• Concluding remarks

The following sections are included:

• General procedure for Lagrangian particle simulation

• SPH code for scalar machines

• SPH code for parallel machines
  • Parallel architectures and parallel computing
  • Parallel SPH code

• A 3D SPH code for solving the N-S equations
  • Main features of the 3D SPH code
  • Conventions for naming variables in FORTRAN
  • Description of the SPH code
  • Two benchmark problems
  • List of the FORTRAN source files

The following sections are included:

• Bibliography

• Index