A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow

04/19/2021
by   Yerbol Palzhanov, et al.
0

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by applications in biomembrane studies, the model is written for tangential flows of fluids constrained to a surface and consists of (surface) Navier-Stokes-Cahn-Hilliard type equations. We apply an unfitted finite element method to discretize the system and introduce a fully discrete time-stepping scheme with the following properties: (i) the scheme decouples the fluid and phase-field equation solvers at each time step, (ii) the resulting two algebraic systems are linear, and (iii) the numerical solution satisfies the same stability bound as the solution of the original system under some restrictions on the discretization parameters. Numerical examples are provided to demonstrate the stability, accuracy, and overall efficiency of the approach. Our computational study of several two-phase surface flows reveals some interesting dependencies of flow statistics on the geometry.

READ FULL TEXT

page 17

page 18

page 19

research
12/08/2021

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

In this article we consider the numerical modeling and simulation via th...
research
02/12/2020

Cahn-Hilliard Navier-Stokes Simulations for Marine Free-Surface Flows

The paper is devoted to the simulation of maritime two-phase flows of ai...
research
05/15/2023

Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows

We develop a method for modeling and simulating a class of two-phase flo...
research
06/23/2021

A Mixed Finite Element Approximation for Fluid Flows of Mixed Regimes in Porous Media

In this paper, we consider the complex flows when all three regimes pre-...
research
07/20/2021

A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches

In this work, we study shape optimization problems in the Stokes flows. ...
research
01/27/2021

Multigrid reduction preconditioning framework for coupled processes in porous and fractured media

Many subsurface engineering applications involve tight-coupling between ...

Please sign up or login with your details

Forgot password? Click here to reset