250 citations · 1.1k across the 130 of their papers we have counts for
6 papers · 2 filters
The finite energy method for compressible fluids. The Navier-Stokes-Korteweg model
Pierre Germain, Philippe G. LeFloch
This is the first of a series of papers devoted to the initial value problem for the Euler system of compressible fluids and augmented versions containing higher-order terms. We en…
High-order asymptotic-preserving methods for fully nonlinear relaxation problems
Sebastiano Boscarino, Philippe G. LeFloch, Giovanni Russo
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit,…
Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation
Philippe G. LeFloch, Hasan Makhlof, Baver Okutmustur
Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz in…
Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical…
Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new frame…
The linear stability of shock waves for the nonlinear Schrödinger-Inviscid Burgers system
Paulo Amorim, Joao-Paulo Dias, Mario Figueira +1
We investigate the coupling between the nonlinear Schrödinger equation and the inviscid Burgers equation, a system which models interactions between short and long waves, for insta…