AN INTRODUCTION TO FINITE VOLUME METHODS FOR HYPERBOLIC CONSERVATION LAWS

Keywords

Conservation law, Finite volume method, Consistency (knowledge bases), Riemann hypothesis, Riemann problem

References

• Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for SourcesFrançois Bouchut — 2005
• Riemann Solvers and Numerical Methods for Fluid DynamicsEleuterio F. Toro — 1997
• Hyperbolic Systems of Conservation LawsAlberto Bressan — 1999
• Finite Volume Methods for Hyperbolic ProblemsR. LeVeque, P. Drazin, M. Ablowitz — 2004
• Finite Volume Methods for Hyperbolic ProblemsRandall J. LeVeque — 2002
• Numerical Approximation of Hyperbolic Systems of Conservation LawsEdwige Godlewski, Pierre-Arnaud Raviart — 2021
• Hyperbolic systems of conservation lawsP. Lax — 2006

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• Modélisation, simulation et assimilation de données autour d'un problème de couplage hydrodynamique-biologieA. Boulanger — 2013
• Modélisation, analyse mathématique et numérique de divers écoulements compressibles ou incompressibles en couche mince.Mehmet Ersoy — 2010
• Étude de schémas numériques pour les écoulements diphasiques en milieu poreux déformable pour des maillages quelconques : application au stockage de déchets radioactifsOphélie Angelini — 2010
• A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation*Emmanuel Audusse, Marie-Odile Bristeau, Benoı̂t Perthame — 2009
• Numerical simulations of a non-hydrostatic shallow water modelMarie-Odile Bristeau, Nicole Goutal, Jacques Sainte-Marie — 2011
• A kinetic interpretation of the section‐averaged Saint‐Venant system for natural river hydraulicsNicole Goutal, Jacques Sainte-Marie — 2011
• A robust and stable numerical scheme for a depth-averaged Euler systemNora Aïssiouene, Marie-Odile Bristeau, Edwige Godlewski — 2015
• Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model: Kinetic interpretation and numerical solutionEmmanuel Audusse, Marie-Odile Bristeau, Marica Pelanti — 2011
• The relativistic Burgers equation on a de Sitter spacetime. Derivation and finite volume approximationBaver Okutmuştur, Tuba Ceylan — 2015
• A combined finite volume - finite element scheme for a dispersive shallow water systemNora Aïssiouene, Marie-Odile Bristeau, Edwige Godlewski — 2015
• NUMERICAL FLOOD SIMULATION BY DEPTH AVERAGED FREE SURFACE FLOW MODELSA.I. Delis, Nikolaos Kampanis — 2010
• Finite volume methods for the one-dimensional shallow water equationsSudi Mungkasi — 2008
• Models and numerical schemes for free surface flows. Beyond the Saint-Venant systemJacques Sainte-Marie — 2010
• A high-order discontinuous Galerkin method for 1D wave propagation in a nonlinear heterogeneous mediumSimon Chabot, Nathalie Glinsky, Diego Mercerat — 2018
• Modélisation numérique de la propagation des ondes par une méthode éléments finis Galerkin discontinue : prise en compte des rhéologies nonlinéaires des solsSimon Chabot — 2018
• Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surfaceS. Allgeyer, Marie-Odile Bristeau, David Froger — 2017
• A two-dimensional method for a family of dispersive shallow water modelsNora Aïssiouene, Marie-Odile Bristeau, Edwige Godlewski — 2019
• Averaged Control Problems Governed by a Semilinear Distributed SystemsRabie Zine, Hamed Ould Sidi, Younes Louartassi — 2023
• One dimensional modelling of Favre waves in channelsBastien Jouy, Damien Violeau, Mario Ricchiuto — 2024
• 2-D Hydrodynamic Simulation of TeraFETs Beyond the Gradual-Channel Approximation for Transient, Large-Signal, or Ultrahigh-Frequency SimulationsFlorian Ludwig, Hartmut G. Roskos, Raul Borsche — 2024

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