Log In Sign Up

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

by   Makrand A Khanwale, et al.

We present a projection-based framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work we extend the fully implicit method presented in Khanwale et al. [A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes., arXiv:2009.06628 (2020)], to a block iterative hybrid method. We use a projection-based semi-implicit time discretization for the Navier-Stokes 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. 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.


page 28

page 30

page 31

page 34

page 40


Fully implicit and accurate treatment of jump conditions for two-phase incompressible Navier-Stokes equation

We present a numerical method for two-phase incompressible Navier-Stokes...

Enhanced Relaxed Physical Factorization preconditioner for coupled poromechanics

In this work, we focus on the relaxed physical factorization (RPF) preco...

Multirate Timestepping for the Incompressible Navier-Stokes Equations in Overlapping Grids

We develop a multirate timestepper for semi-implicit solutions of the un...

Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics

We present a hybrid mimetic finite-difference and virtual element formul...