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. 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.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- October 2020
- DOI:
- 10.1016/j.jcp.2020.109674
- arXiv:
- arXiv:1912.12453
- Bibcode:
- 2020JCoPh.41909674K
- Keywords:
-
- Two-phase flows;
- Energy stable;
- Adaptive finite elements;
- Octrees;
- Scalable;
- Mathematics - Numerical Analysis;
- Physics - Computational Physics;
- Physics - Fluid Dynamics
- E-Print:
- 59 pages, 22 figures, submitted to Journal of Computational Physics