Campus Units
Mechanical Engineering, Electrical and Computer Engineering, Plant Sciences Institute, Mathematics
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
2020
Journal or Book Title
arXiv
Abstract
We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et al. [{\it Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes}, J. Comput. Phys. (2020)], to a fully-coupled, provably second-order accurate scheme in time, while maintaining energy-stability. The new method requires fewer matrix assemblies in each Newton iteration resulting in faster solution time. The method is based on a fully-implicit Crank-Nicolson scheme in time and a pressure stabilization for an equal order Galerkin formulation. That is, we use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) procedure to stabilize the pressure. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise, Rayleigh-Taylor instability, and lid-driven cavity flow problems. We analyze in detail the scaling of our numerical implementation.
Copyright Owner
The Author(s)
Copyright Date
2020
Language
en
File Format
application/pdf
Recommended Citation
Khanwale, Makrand A.; Saurabh, Kumar; Fernando, Milinda; Calo, Victor M.; Rossmanith, James A.; Sundar, Hari; and Ganapathysubramanian, Baskar, "A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes" (2020). Mechanical Engineering Publications. 436.
https://lib.dr.iastate.edu/me_pubs/436
Comments
This is a pre-print of the article Khanwale, Makrand A., Kumar Saurabh, Milinda Fernando, Victor M. Calo, James A. Rossmanith, Hari Sundar, and Baskar Ganapathysubramanian. "A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes." arXiv preprint arXiv:2009.06628 (2020). Posted with permission.