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arXiv · 2009.06628

A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes

Makrand A Khanwale·Kumar Saurabh·Milinda Fernando·Victor M. Calo·James A. Rossmanith·Hari Sundar·Baskar Ganapathysubramanian
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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. [\textit{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.

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Makrand A Khanwale, Kumar Saurabh, Milinda Fernando, Victor M. Calo, James A. Rossmanith, Hari Sundar, Baskar Ganapathysubramanian. 2022-08-13. A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes. https://doi.org/10.1016/j.cpc.2022.108501

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