The layer-averaged Euler system with variable density

For more info about our services contact : help@bestpfe.com

Table of contents

Abstract
Contents
List of Figures
Introduction
Context
Sediment transport
Variable density flows
Contributions
Modeling and simulation of sediment transport
Modeling and simulation of variable density flows
Outline of the conclusion and perspectives
Modeling and simulation of sediment transport
Modeling and simulation of variable density flows
Common perspectives
I Sediment transport
1 Existing models based on the Shallow Water equations
1.1 The Shallow Water equations
1.2 The Exner equation
1.2.1 The transport threshold
1.2.2 Some bed load transport formulae
1.2.3 Critics made to the bed load transport formulae
1.3 Possible improvements to the Exner model
1.3.1 Necessity of a phase shift
1.3.2 Improvement of the flow model
1.3.3 Improved description of the sediment layer
1.3.4 Non-local models for other applications
1.4 Numerical resolution of the Shallow Water-Exner system
2 A non-local sediment transport model
2.1 Overview of the water-sediment system
2.1.1 Bilayer Navier-Stokes equations
2.1.2 Introduction of a threshold for the onset of motion
2.2 The sediment layer integrated model
2.2.1 Vertically averaged models
2.2.2 Numerical scheme
2.2.3 Numerical validation
2.3 Coupled water and sediment system
2.3.1 Modeling of the coupled system
2.3.2 Numerical strategy for the coupled system
2.3.3 Numerical results for the coupled system
2.4 Other numerical schemes
2.4.1 A scheme for the local model
2.4.2 Extension for the non-local model
2.5 Conclusions and perspectives
List of main symbols used in Chapter 2
II The Navier-Stokes system with temperature and salinity for free-surface flows
3 Low-Mach approximation & layer-averaged formulation
3.1 Introduction
3.2 The 3d Navier-Stokes-Fourier system
3.2.1 The compressible Navier-Stokes-Fourier system
3.2.2 Boundary conditions
3.2.3 The incompressible limit
3.2.4 The Navier-Stokes-Fourier system with salinity
3.2.5 The Euler-Fourier system
3.2.6 The hydrostatic assumption
3.2.7 The Boussinesq assumption
3.3 The layer-averaged models
3.3.1 The layer-averaged Euler system with variable density
3.3.2 The layer-averaged Navier-Stokes-Fourier system
3.4 Conclusion
Acknowledgments
4 Numerical scheme and validation
4.1 Introduction
4.2 The layer-averaged models
4.2.1 The multilayer Navier-Stokes-Fourier model
4.2.2 The layer-averaged Euler-Fourier system
4.3 Numerical scheme for the layer-averaged Euler-Fourier system
4.3.1 Strategy for the time discretization
4.3.2 Semi-discrete (in time) scheme
4.3.3 Finite volume formalism for the Euler part
4.3.4 Kinetic fluxes
4.3.5 Discrete entropy inequality
4.4 Numerical scheme for the layer-averaged Navier-Stokes-Fourier system .
4.4.1 Semi-discrete (in time) scheme
4.4.2 Spatial discretization of the diffusion terms
4.5 Numerical validation
4.5.1 Analytic solution
4.5.2 Lock exchange
4.5.3 Diffusion
4.6 Conclusion
Acknowledgments
List of main symbols in Chapters 3 and 4
Bibliography