Orateur : Firas Dhaouadi
Établissement : Laboratory of Applied Mathematics (University of Trento) (Italie)
Dates : 2025-02-20 – 2025-02-20
Heures : 14:00 – 14:00
Lieu : Salle 12 (H06)
Résumé :
I will present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques, with a classical Cattaneo-type relaxation that allows to reformulate diffusion equations as augmented first order hyperbolic systems with stiff relaxation source terms. The proposed system is proven to be hyperbolic and to admit a Lyapunov functional, in accordance with the original equations.
I will also present a new numerical scheme to solve the original Cahn-Hilliard equations based on conservative semi-implicit finite differences, to obtain reference solutions.
The corresponding hyperbolic system is numerically solved by means of a classical second order MUSCL-Hancock-type finite volume scheme. The proposed approach is
validated through a set of classical benchmarks such as spinodal decomposition, Ostwald ripening in one and two dimensions of space and exact stationary solutions.
In particular for spinodal decomposition, I will present a homemade deterministic test case.