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Title: Simplified conservative discretization of the Cahn-Hilliard-Navier-Stokes equations
In this paper we construct a novel discretization of the Cahn-Hilliard equation coupled with the Navier-Stokes equations. The Cahn-Hilliard equation models the separation of a binary mixture. We construct a very simple time integration scheme for simulating the Cahn-Hilliard equation, which is based on splitting the fourth-order equation into two second-order Helmholtz equations. We combine the Cahn-Hilliard equation with the Navier-Stokes equations to simulate phase separation in a two-phase fluid flow in two dimensions. The scheme conserves mass and momentum and exhibits consistency between mass and momentum, allowing it to be used with large density ratios. We introduce a novel discretization of the surface tension force from the phase-field variable that has finite support around the transition region. The model has a parameter that allows it to transition from a smoothed continuum surface force to a fully sharp interface formulation. We show that our method achieves second-order accuracy, and we compare our method to previous work in a variety of experiments.  more » « less
Award ID(s):
2006570
PAR ID:
10558585
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal of Computational Physics
Volume:
519
Issue:
C
ISSN:
0021-9991
Page Range / eLocation ID:
113382
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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