250 citations · 1.1k across the 130 of their papers we have counts for
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A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport
Hasan Karjoun, Abdelaziz Beljadid, Philippe G. LeFloch
We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Nov…
A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background
Philippe G. LeFloch, Carlos Parés, Ernesto Pimentel-García
For the evolution of a compressible fluid in spherical symmetry on a Schwarzschild curved background, we design a class of well-balanced numerical algorithms with first-order or se…
Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based…
Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts
Philippe G. LeFloch, Hendrik Ranocha
We study nonlinear hyperbolic conservation laws with non-convex flux in one space dimension and, for a broad class of numerical methods based on summation by parts operators, we co…
Universal scattering laws for quiescent bouncing cosmology
Bruno Le Floch, Philippe G. LeFloch, Gabriele Veneziano
Cosmological bounces occur in many gravity theories. We define singularity scattering maps relating large scale geometries before and after the bounce (assuming no BKL oscillations…
A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes
Florian Beyer, Philippe G. LeFloch
We consider a class of Fuchsian equations that, for instance, describes the evolution of compressible fluid flows on a cosmological spacetime. Using the method of lines, we introdu…