Convergence and error estimates

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Table of contents

1 La méthode ”Upwind Interface Source” pour les lois de conservation hyperboliques
1 Convergence of the Upwind Interface Source method for hyperbolic conservation laws
1 Introduction
2 Upwind Interface Source method
3 Well-balancedschemes
4 Consistency
5 ALax-Wendroff type convergence theorem
6 Conclusion
References
2 First and second order error estimates for the Upwind Interface Source method
1 Introduction
1.1 Formalism of the Upwind Interface Source method
1.2 What is a second order scheme for the Upwind Interface Source method ?
1.3 Convergence and error estimates
2 Errorestimatesforfirstorderschemes
2.1 Stability estimate
2.2 Consistency estimate
2.3 Proof of Theorem 1.2
3 Errorestimatesforsecondorderschemes
3.1 Stability estimate
3.2 Consistency estimate
3.3 Proof of Theorem 1.3 and Theorem 1.4
4 Remarks and numerical evidence
References
2 L’approximation num´erique des ´equations de Saint- Venant et applications aux ´etudes exp´erimentales
3 A kinetic scheme for the Saint-Venant system with a source term 
1 Introduction
2 Preliminaries about the Saint-Venant equations
2.1 Properties of the system
2.2 Kinetic approach
3 Thekineticschemewithreflections
3.1 The formulas
3.2 Properties of the numerical scheme
4 Numerical implementation
4.1 Computation of the integrals
4.2 Some numerical tests
References
4 Second order approximation of the viscous Saint-Venant system and comparison with experiments 
1 Introduction
2 Formalism of the numerical method
3 Secondorderschemes
4 Experimental configuration and numerical results
References
Appendice
5 Numerical modelling of avalanches based on Saint-Venant equations using kinetic scheme 
1 Introduction
2 Equations
3 Flow and friction law
3.1 Simple friction law
3.2 Flow variable friction law
4 Numerical model
4.1 Finite volume method
4.2 Kinetic formulation
4.3 Friction
5 Validation
6 One-dimensionalsimulationoversimplifiedtopography
6.1 Curvature effects
6.2 The Coulomb friction law
6.3 Pouliquen’s friction law
6.4 Mass stopping
7 Conclusion
References