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:
- Spatial discretization: continuous finite elements with variational multiscale (VMS) based stabilization;
- Temporal discretization: efficient implicit and semi-implicit schemes that are energy stable and mass conserving. energy stability and mass conservation; and
- 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.