In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems 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.
| Identifer | oai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-00651688 |
| Date | 12 December 2011 |
| Creators | Ricchiuto, Mario |
| Publisher | Université Sciences et Technologies - Bordeaux I |
| Source Sets | CCSD theses-EN-ligne, France |
| Language | English |
| Detected Language | English |
| Type | habilitation à ¤iriger des recherches |
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