7 papers
Energy consistent hyperbolic approximation for a class of fourth-order partial differential equations
Rahul Barthwal, Firas Dhaouadi, Christian Rohde
In this article, we propose a novel hyperbolic relaxation system for a general class of fourth-order nonlinear partial differential equations arising in the modelling of thin film…
Analysis and structure-preserving discretization of the Heat-GLM system
Firas Dhaouadi, Laura Río-Martín, Michael Dumbser
In this paper, we study a prototype hyperbolic system arising from the coupling of Generalized-Lagrangian-Multiplier (GLM) curl-cleaning with linear acoustics. We first show that,…
On hyperbolic approximations for a class of dispersive and diffusive-dispersive equations
Rahul Barthwal, Firas Dhaouadi, Christian Rohde
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictl…
Structure Preserving Finite Volume Schemes on Voronoi Grids: Curl Involution, Asymptotic Limit and Thermodynamics
Walter Boscheri, Firas Dhaouadi
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form…
A first-order hyperbolic reformulation of the Cahn-Hilliard equation
Firas Dhaouadi, Michael Dumbser, Sergey Gavrilyuk
In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques pro…
An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model
Laura Río-Martín, Firas Dhaouadi, Michael Dumbser
We present a new second order accurate structure-preserving finite volume scheme for the solution of the compressible barotropic two-phase model of Romenski et. al in multiple spac…