VMS-stabilized continuous Galerkin finite element methods for the Cahn-Hilliard Navier-Stokes (CHNS) phase-field model of multiphase flows

The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can effectively capture interfacial dynamics in multi-phase fluid flows. The goal of this work is to develop a class of numerical methods with several key properties: 

  1. Spatial discretization: continuous finite elements with variational multiscale (VMS) based stabilization;
  2. Temporal discretization: efficient implicit and semi-implicit schemes that are energy stable and mass conserving. energy stability and mass conservation; and
  3. Implementation: massively parallel numerical implementation using parallel octree-based adaptive meshes. 

Past work has focused on two-phase flows; current work is focused on extensions to multi-phase flows.