250 citations · 1.1k across the 130 of their papers we have counts for
5 papers · 2 filters
Why many theories of shock waves are necessary. Kinetic functions, equivalent equations, and fourth-order models
Philippe G. LeFloch, Majid Mohammadian
We consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena. These models admit under…
The minimum entropy principle for fluid flows in a nozzle with discontinuous cross-section
Dietmar Kroener, Philippe G. LeFloch, Mai-Duc Thanh
We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system…
Convergent and conservative schemes for nonclassical solutions based on kinetic relations
Benjamin Boutin, Christophe Chalons, Frederic Lagoutiere +1
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative a…
Finite volume schemes on Lorentzian manifolds
Paulo Amorim, Philippe G. LeFloch, Bawer Okutmustur
We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishe…
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
Philippe G. LeFloch, Jian-Guo Liu
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increa…