An unconditionally stable hybrid discontinuous Galerkin scheme for a Cahn–Hilliard phase-field model of two-phase incompressible flow with variable densities

Changlun Ye, Hai Bi and Xianbing Luo

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 403-419

Abstract: In this paper, we establish a new hybrid discontinuous Galerkin scheme for the Abels–Garcke–Grün (AGG) model, a thermodynamically consistent phase-field model for two-phase incompressible flows with variable densities. The scheme possesses the following features: (i) Linearity and full decoupling; (ii) The introduction of a new hybrid discontinuous stabilization term in the Cahn–Hilliard equation, designed to balance the explicit treatment of the coupling term, and the discretization of convection terms in the Navier–Stokes equations using a DG-based upwinding technique with post-processed chemical potential and phase variables; (iii) The generation of a globally divergence-free velocity approximation; (iv) Efficient implementation via static condensation. We rigorously prove that the scheme has a unique solution and is unconditionally energy stable. Finally, we present several numerical examples to demonstrate the efficiency of the proposed scheme. Additionally, the scheme proves to be robust in high Reynolds number cases.

Keywords: Hybrid discontinuous Galerkin; Two-phase incompressible flows; Variable density; Divergence-free velocity approximation; Phase-field model (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:403-419

DOI: 10.1016/j.matcom.2025.05.028

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