tel-00651688, version 1

Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows

Mario Ricchiuto () ^1, 2

Université Sciences et Technologies - Bordeaux I (12/12/2011), Alain Lerat (Pr.)

• 1 :  BACCHUS (INRIA Bordeaux - Sud-Ouest)
• 
  INRIA – Université de Bordeaux – CNRS : UMR5800 France
• 2 :  Institut de Mathématiques de Bordeaux (IMB)
• http://www.math.u-bordeaux.fr/IMB/
  CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II 351 cours de la Libération 33405 TALENCE CEDEX France

Références bibliographiques

• Type de publication : HDR
• titre : Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows
• titre en anglais : Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows
• date de soutenance : 12/12/2011
• résumé : 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.
• 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 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.
• domaine :

  Mathématiques/Analyse numérique

  Sciences de l'environnement

  Sciences de l'ingénieur/Mécanique/Mécanique des fluides

  Physique/Mécanique/Mécanique des fluides

• organisme de délivrance : Université Sciences et Technologies - Bordeaux I
• langue : Anglais
• président du jury : Alain Lerat
• courriel du président : alain.LERAT@ensam.eu
• composition du Jury : Remi Abgrall (director),
  Mejdi Azaiez (membre invité)
  Thierry Colin (reviewer)
  Alexandre Ern (reviewer)
  Alain Lerat (president)
  Luc Mieussens (membre invité)
  Claus-Dieter Munz (reviewer)
• mots-clés : Numerical analysis – hyperbolic problems – unstructured grids – finite elements – residual based schemes – high order schemes – time dependent problems – free surface flow – shallow water equations – positivity preservation – source terms – C-property – super consistency – long wave run up simulations – tsunami simulations
• mots-clés en anglais : Numerical analysis, hyperbolic problems, unstructured grids, finite elements, residual based schemes, high order schemes, time dependent problems, free surface flow, shallow water equations, positivity preservation, source terms, C-property, super consistency, long wave run up simulations, tsunami simulations

Liste des fichiers attachés à ce document :

• tel-00651688, version 1
• http://tel.archives-ouvertes.fr/tel-00651688
• oai:tel.archives-ouvertes.fr:tel-00651688
• Contributeur : Mario Ricchiuto <>
• Soumis le : Jeudi 15 Décembre 2011, 14:24:46
• Dernière modification le : Mercredi 21 Décembre 2011, 15:20:26