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

TL;DR

This paper presents a thermodynamically consistent, energy-stable numerical method for simulating two-phase flows with deforming interfaces, utilizing adaptive octree meshes and validated through extensive numerical experiments.

Contribution

It introduces an energy-stable Crank-Nicolson scheme for Cahn-Hilliard Navier-Stokes equations with a parallel adaptive mesh implementation and provides rigorous stability proofs.

Findings

The scheme is unconditionally energy-stable and convergent.

Numerical experiments validate the method against experimental data.

The approach scales efficiently on parallel computing architectures.

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.