A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2023

A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities

Abstract

A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a second-order phase-field approximation for surface diffusion flows. Its numerical discretization is challenging due to the degeneracy of the mobilities, which generally requires an implicit treatment to avoid stability issues at the price of increased complexity costs. To mitigate this drawback, we consider new first- and second-order Scalar Auxiliary Variable (SAV) schemes that, differently from existing approaches, focus on the relaxation of the mobility, rather than the Cahn-Hilliard energy. These schemes are introduced and analysed theoretically in the general context of gradient flows and then specialised for the Cahn-Hilliard equation with mobilities. Various numerical experiments are conducted to highlight the advantages of these new schemes in terms of accuracy, effectiveness and computational cost.

Dates and versions

hal-04294086 , version 1 (19-11-2023)

Identifiers

Cite

Elie Bretin, Luca Calatroni, Simon Masnou. A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities. Discrete and Continuous Dynamical Systems - Series S, 2023, ⟨10.3934/dcdss.2023177⟩. ⟨hal-04294086⟩
66 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More