Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes

Abstract

We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable Crank-Nicolson-type time integration scheme is used. Detailed proofs of energy stability of the semi-discrete scheme and for the existence of solutions of the advective-diffusive Cahn-Hilliard operator are provided. In space we discretize with a conforming continuous Galerkin finite element method in conjunction with a residual-based variational multi-scale (VMS) approach in order to provide pressure stabilization. We deploy this approach on a massively parallel numerical implementation using fast octree-based adaptive meshes. A detailed scaling analysis of the solver is presented. Numerical experiments showing convergence and validation with experimental results from the literature are presented for a large range of density ratios.

arXiv comment59 pages, 22 figures, submitted to Journal of Computational Physics; Version accepted by the journal

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• Assessment of an energy-based surface tension model for simulation of two-phase flows using second-order phase field methods
• A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow
• Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities
• Accurate calculation of bubble and droplet properties in diffuse-interface two-phase simulations