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

• Published in: Journal of computational physics 2020-10, Vol.419, p.109674, Article 109674
• Main Authors: Khanwale, Makrand A., Lofquist, Alec D., Sundar, Hari, Rossmanith, James A., Ganapathysubramanian, Baskar
• Format: Article
• Language: English
• Subjects: Adaptive finite elements; Computational fluid dynamics; Computational physics; Density; Energy stable; Finite element method; Fluid flow; Navier-Stokes equations; Octrees; Scalable; Time integration; Two phase flow; Two-phase flows
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.109674

•Two-phase flows simulated using thermodynamically consistent Cahn-Hilliard Navier-Stokes equations.•Provably energy-stable Crank-Nicolson-type time integration scheme.•Continuous Galerkin finite element with variational multi-scale (VMS) used.•Deployed a parallel numerical implementation using fast octree-based adaptive meshes. 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. We discretize spatial terms 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.