
Numerical Simulation of the Gravity-Inertial Spreading of Oil Using Smoothed Particle Hydrodynamics
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Content
- Intro
- Contents
- List of Figures
- List of Tables
- List of Symbols and Abbreviations
- Preface
- Chapter 1
- 1.1 Motivation
- 1.2 Brief Considerations on the Scientific Method
- 1.3 Numerical Methods
- 1.4 Eulerian Approach
- 1.4.1 Fay's Spreading Model
- 1.4.1.1 Physical Analysis of the Forces
- 1.4.1.2 Physical-Mathematical Modelling
- 1.4.1.3 Revised Fay's Spreading Model
- 1.4.2 Blokker's Spreading Model
- 1.5 Lagrangian Approach
- 1.6 Hybrid Models
- 1.7 Purely Lagrangian Smoothed Particle Hydrodynamics Method
- 1.8 Final Considerations about the Modelling of Spreading of Oil
- 1.9 Presentation of the Remaining Chapters
- References
- Chapter 2
- 2.1 The Continuum Hypothesis
- 2.2 Mathematical Fundamentals
- 2.2.1 Approximation of the Divergent of a Vectorial Function
- 2.2.2 Approximation of the Gradient of a Scalar Function
- 2.2.3 Approximation of the Laplacian of a Scalar Function
- 2.2.4 Errors in SPH Approximations
- 2.2.5 Smoothing Functions
- 2.3 Conservation Equations and SPH Approximations
- 2.3.1 Physical Conservation Equations
- 2.3.1.1 Pressure Modelling
- 2.3.1.2 Specific Internal Energy
- 2.3.2 SPH Approximations for the Conservation Equations
- 2.3.2.1 Mass Conservation
- 2.3.2.2 Momentum Conservation
- 2.4 Search for Neighbouring Particles
- 2.5 Treatment of the Free Surfaces
- 2.5.1 Continuum Surface Force Method
- 2.5.2 Free Surface Identification Using a Parameter
- 2.5.3 Surface Particle Tracking Using the Divergence of the Particles' Positions
- 2.6 Contact Algorithm for Interface Treatment
- 2.6.1 Inter-Particle Collisions Considerations in SPH Simulations
- 2.7 Turbulence
- 2.8 Diffusive Terms in SPH Approximation for the Momentum Conservation Equation
- 2.9 Temporal Integration
- 2.9.1 Euler Integration Scheme (First Order Runge-Kutta)
- 2.9.2 Leap-Frog Integrator
- 2.9.3 Predictor-Corrector Method
- 2.9.4 Simulation Time Step
- 2.9.4.1 Variable Time Step
- 2.10 Consistency
- 2.10.1 Restoration of the Consistency
- 2.10.1.1 Corrective Smoothed Particle Method (CSPM)
- 2.10.1.2 Mean Least Squares (MLS) Method
- 2.10.1.3 Kernel Gradient Correction Method
- 2.11 Numerical Aspects
- 2.11.1 Support Radius Length (Smoothing Length Update)
- 2.11.2 Numerical Corrections
- 2.11.2.1 Artificial Viscosity
- 2.11.2.2 XSPH Correction
- 2.11.2.3 Tensile Instability
- 2.12 Initial and Boundary Conditions
- 2.12.1 Repulsive Boundary Conditions
- 2.12.2 Dynamic Boundary Conditions
- 2.12.3 Semi-analytical Boundary Conditions
- 2.12.4 Reflective Boundary Conditions
- 2.12.4.1 Algorithmic Methodology
- 2.12.4.2 Newton's Restitution Law and Friction
- 2.12.4.3 Collision Response
- 2.12.5 Periodic Open Boundary Conditions
- 2.13 Numerical Code
- References
- Chapter 3
- 3.1 Heat Diffusion in a Homogeneous Flat Plate
- 3.1.1 Computational Domain and Particle Discretisation
- 3.1.2 Initial Conditions, Boundary Conditions and Simulation Parameters
- 3.1.3 Results and Discussions
- 3.2 Still Liquid inside an Immobile Reservoir
- 3.2.1 Computational Domain and Particle Discretisation
- 3.2.2 Initial and Boundary Conditions
- 3.2.3 Implementation of Boundary Treatment Using Virtual Particles
- 3.2.3.1 Results and Discussions
- 3.2.4 Reflective Boundary Treatment
- 3.2.4.1 Results and Discussions
- 3.3 Dam-Breaking Over a Dry Bed
- 3.3.1 Computational Domain and Particle Discretisation
- 3.3.2 Initial Conditions, Boundary Conditions and Simulation Parameters
- 3.3.3 Results and Discussions
- References
- Chapter 4
- 4.1 Introduction
- 4.2 Simulated Geometry, Initial Conditions and Boundary Conditions
- 4.2.1 Interface Treatment
- 4.3 Results and Discussion
- 4.4 Final Remarks
- References
- Chapter 5
- Appendix
- Index
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