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

Mario Ricchiuto

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.)

Abstract: 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.

1: BACCHUS (INRIA Bordeaux - Sud-Ouest)
INRIA – Université de Bordeaux – CNRS : UMR5800
2: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II

tel-00651688, version 1
http://tel.archives-ouvertes.fr/tel-00651688
oai:tel.archives-ouvertes.fr:tel-00651688
From: Mario Ricchiuto <>
Submitted on: Thursday, 15 December 2011 14:24:46
Updated on: Wednesday, 21 December 2011 15:20:26

See detailed view

Associated documents

PDF :

Export

Bibtex EndNote TEI RefWorks

%F tel-00651688, version 1
%0 Thesis
%U http://tel.archives-ouvertes.fr/tel-00651688
%T Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows
%A Ricchiuto, Mario
%+ BACCHUS - INRIA Bordeaux - Sud-Ouest , Institut de Mathématiques de Bordeaux - IMB
%T Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows
%8 2011-12-12
%X 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.
%X 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.
%2 MATH:MATH_NA;SDE;SPI:MECA:MEFL;PHYS:MECA:MEFL
%I Université Sciences et Technologies - Bordeaux I
%G English
%Z Alain Lerat
%Z alain.LERAT@ensam.eu
%Z Remi Abgrall (director),Mejdi Azaiez (membre invité)Thierry Colin (reviewer)Alexandre Ern (reviewer)Alain Lerat (president)Luc Mieussens (membre invité)Claus-Dieter Munz (reviewer)
%K 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
%K 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