A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow

02/21/2020

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by   Guosheng Fu, et al.

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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.