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SIAM Journal on Scientific Computing, ISSN 1064-8275, 2012, Volume 34, Issue 5, pp. B523 - B558
Journal Article
Communications in Computational Physics, ISSN 1815-2406, 04/2017, Volume 21, Issue 4, pp. 913 - 946
We propose here a class of numerical schemes for the approximation of weak solutions to nonlinear hyperbolic systems in nonconservative form-the notion of... 
discrete scheme | complex fluid dynamics | nonconservative system | Nonlinear hyperbolic | controlled dissipation | NUMERICAL-METHODS | KINETIC RELATIONS | EXISTENCE | PHYSICS, MATHEMATICAL | NONCLASSICAL SHOCKS | WAVES | MODELS | PRODUCTS | ERROR | CONSERVATION-LAWS
Journal Article
Computers and Fluids, ISSN 0045-7930, 06/2018, Volume 169, pp. 10 - 22
It is well known, thanks to Lax–Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and... 
Nonconservative formulation | Euler equations | Fluid dynamics | Residual distribution | Multiphase flow systems | Conservation | RELAXATION-PROJECTION METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | COMPRESSIBLE FLOWS | MESHES | RESIDUAL DISTRIBUTION SCHEMES
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 1/2007, Volume 41, Issue 1, pp. 169 - 185
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal... 
Approximate Riemann solvers | Nonconservative hyperbolic systems | Godunov method | Well-balancing | approximate Riemann solvers | SOURCE TERMS | DEFINITION | MATHEMATICS, APPLIED | well-balancing | nonconservative hyperbolic systems | WELL-BALANCED SCHEME | CONSERVATION-LAWS
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 9/2004, Volume 38, Issue 5, pp. 821 - 852
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to... 
Source terms | Well-balanced schemes | Nonconservative hyperbolic systems | Shallow-water systems | Roe method | MATHEMATICS, APPLIED | well-balanced schemes | EQUATIONS | IRREGULAR GEOMETRY | FORMULATION | RIEMANN PROBLEM | SCHEME | shallow-water systems | PRODUCTS | nonconservative hyperbolic systems | source terms | CHANNELS | CONSERVATION-LAWS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 01/2016, Volume 272, pp. 385 - 402
•Unsplit implementation of hyperbolic divergence cleaning•Galilean invariant hyperbolic divergence cleaning (= Powell+GLM)•Via Roe-linearization full control... 
Generalized Lagrange multiplier | Shallow water MHD | Finite-volume schemes | Divergence cleaning | Nonconservative PDE | MATHEMATICS, APPLIED | SOLVERS | MHD EQUATIONS | NonconseNative PDE | CONSTRAINED TRANSPORT METHOD | IDEAL MHD | SYSTEMS | CONSERVATION-LAWS | FLOWS | Fluid dynamics
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 10/2012, Volume 75, Issue 15, pp. 5933 - 5960
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2000, Volume 39, Issue 9, pp. 135 - 159
We propose a way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of balance... 
Conservation laws | Source terms | Nonconservative products | Balanced scheme | MATHEMATICS, APPLIED | GODUNOV | conservation laws | RIEMANN SOLVER | EQUATIONS | nonconservative products | ROE | source terms | balanced scheme | FLOWS
Journal Article
Computers and Fluids, ISSN 0045-7930, 08/2016, Volume 134-135, pp. 111 - 129
Journal Article
Journal of Computational Science, ISSN 1877-7503, 01/2013, Volume 4, Issue 1-2, pp. 111 - 124
► Nonconservative hyperbolic systems. ► Dal Maso–LeFloch–Murat path theory. ► Numerical approximation of non-conservative systems. Attempts to define weak... 
Lax–Friedrichs scheme | Godunov scheme | Nonconservative product | Finite volume schemes | Hyperbolic systems | Lax-Friedrichs scheme | RIEMANN SOLVER | EQUATIONS | MODEL | SHOCK-WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERROR | COMPUTER SCIENCE, THEORY & METHODS | FLOWS | SCHEMES
Journal Article
Multiscale Modeling and Simulation, ISSN 1540-3459, 2011, Volume 9, Issue 3, pp. 1253 - 1275
Journal Article