We construct a divergence-free HDG scheme for the Cahn-Hilliard-Navier-Stokes phase field model. The scheme is robust in the convection-dominated regime, produce a globally divergence-free velocity approximation, and can be efficiently implemented via static condensation. Two numerical benchmark problems, namely the rising bubble problem, and the Rayleigh-Taylor instability problem are used to show the good performance of the proposed scheme.
@article{arxiv.2002.09150,
title = {A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow},
author = {Guosheng Fu},
journal= {arXiv preprint arXiv:2002.09150},
year = {2020}
}