Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows
RICCHIUTO, Mario
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
RICCHIUTO, Mario
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
HDR
Résumé en anglais
In this work we review 12 years of developments in the field of residual based discretizations and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled ...Lire la suite >
In this work we review 12 years of developments in the field of residual based discretizations and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach.< Réduire
Mots clés
analyse numérique
éléments finis
écoulements a surface libre
C-property
schémas d'ordre élévé
preservation de la monotonie
preservation de la positivité
Mots clés en anglais
numerical analysis
finite elements
free surface flows
high order schemes
monotonicity preservation
positivity preservation
Origine
Importé de halUnités de recherche