48 citations · 89 across the 6 of their papers we have counts for
8 papers
Stability theory for some scalar finite difference schemes : Validity of the modified equations approach
Firas Dhaouadi, Emilie Duval, Sergey Tkachenko +1
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative e…
Augmented Skew-Symetric System for Shallow-Water System with Surface Tension Allowing Large Gradient of Density
Jean-Paul Vila, Gael Richard, Didier Bresch +7
In this paper, we introduce a new extended version of the shallow water equations with surface tension which is skew-symmetric with respect to the L2 scalar product and allows for…
An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification
Frédéric Couderc, Arnaud Duran, Jean-Paul Vila
We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy i…
Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and applications
Didier Bresch, Pascal Noble, Jean-Paul Vila
Recently, A. Vasseur and C. Yu have proved the existence of global entropy-weak solutions to the compressible Navier-Stokes equations with viscosities and $λ(…
New Extended Formulations of Euler-Korteweg Equations Based on a Generalization of the Quantum Bohm Identity
Didier Bresch, Frédéric Couderc, Pascal Noble +1
In this note, we propose an original extended formulation of Euler-Korteweg systems based on a generalization of the quantum Bohm potential identity. This new formulation allows to…
Stability theory for difference approximations of some dispersive shallow water equations and application to thin film flows
Pascal Noble, Jean-Paul Vila
In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system per…