A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes
Abstract
The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can be used to effectively capture interfacial dynamics in two-phase fluid flows. In this work, we present a semi-implicit, projection-based finite element framework for solving the CHNS system. We use a projection-based semi-implicit time discretization for the Navier-Stokes equation and a fully-implicit time discretization for the Cahn-Hilliard equation. We use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) formulation. Pressure is decoupled using a projection step, which results in two linear positive semi-definite systems for velocity and pressure, instead of the saddle point system of a pressure-stabilized method. All the linear systems are solved using an efficient and scalable algebraic multigrid (AMG) method. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. The overall approach allows the use of relatively large time steps with much faster time-to-solve than similar fully-implicit methods. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise and Rayleigh-Taylor instability.
Keywords
Cite
@article{arxiv.2107.05123,
title = {A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes},
author = {Makrand A. Khanwale and Kumar Saurabh and Masado Ishii and Hari Sundar and James A. Rossmanith and Baskar Ganapathysubramanian},
journal= {arXiv preprint arXiv:2107.05123},
year = {2023}
}
Comments
51 pages, 18 Figures, version accepted for publication Journal of Computational Physics. arXiv admin note: text overlap with arXiv:2009.06628