Fully discrete entropy inequality

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

Table of contents

1 Introduction 
1.1 General issues
1.2 Applications and motivations
1.3 Geophysical models
1.4 Numerical methods
1.5 Outline of the main contributions of this PhD thesis
1.6 Outline of the conclusion
1.7 Future work
2 A robust and stable numerical scheme for a depth-averaged Euler system 
2.1 Introduction
2.2 A depth-averaged Euler system
2.3 Kinetic description
2.4 Numerical scheme
2.5 Fully discrete entropy inequality
2.6 Analytical solutions
2.7 Numerical simulations
2.8 Conclusion
3 A combined finite volume/ finite element method for a 1D dispersive Shallow Water system 
3.1 Introduction
3.2 The projection scheme for the non-hydrostatic model
3.3 Numerical approximation
3.4 Analytical solutions
3.5 Numerical results
3.6 Conclusion
4 A numerical method for a two-dimensional dispersive shallow water system on unstructured grids 
4.1 Introduction
4.2 The model
4.3 Time and space discretizations
4.4 The mixed problem
4.5 Finite element approximations for the mixed problem
4.6 Numerical algorithm
4.7 Validation with analytical solutions
4.8 Numerical results
4.9 Conclusion
5 Supplementary results 
5.1 Introduction
5.2 Stationary solutions for the one-dimensional problem
5.3 Another analytical solution
5.4 Dispersion relation
5.5 Breaking wave
5.6 Conclusion
A A coupled Exner/ Stokes model 
A.1 Introduction
A.2 The model
A.3 Variational formulation
A.4 Numerical tests
A.5 Conclusion