Schéma nonlinéaire pour l'approximation numérique d'un système hyperbolique non conservatif. (Nonlinear scheme to approximate nonconservative hyperbolic system)

DOI10.1016/S1631-073X(02)02615-8zbMath1018.65107MaRDI QIDQ1565933

Christophe Berthon

Publication date: 27 May 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

consistencyconservation lawsfinite volume methodBurgers equationRiemann problemdiffusion tensornonconservative hyperbolic systembifluid flowdiscontinuous shock wave solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems -- second-order extension ⋮ Entropy-stable space–time DG schemes for non-conservative hyperbolic systems ⋮ A new comment on the computation of non-conservative products using Roe-type path conservative schemes ⋮ Unnamed Item ⋮ WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE ⋮ On the numerical solution of nonconservative hyperbolic systems of equations ⋮ Application of averaging techniques to traffic flow theory ⋮ Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows ⋮ Numerical methods with controlled dissipation for small-scale dependent shocks

Cites Work

• Numerical approximation of hyperbolic systems of conservation laws
• Definition and weak stability of nonconservative products
• AQ-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system
• Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
• A NONCONSERVATIVE HYPERBOLIC SYSTEM MODELING SPRAY DYNAMICS. PART I: SOLUTION OF THE RIEMANN PROBLEM
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