The Coupled Volume of Fluid and Brinkman Penalization Methods for Simulation of Incompressible Multiphase Flows

Abstract

In this work, we contribute to the development of numerical algorithms for the direct simulation of three-dimensional incompressible multiphase flows in the presence of multiple fluids and solids. The volume of fluid method is used for interface tracking, and the Brinkman penalization method is used to treat solids; the latter is assumed to be perfectly superhydrophobic or perfectly superhydrophilic, to have an arbitrary shape, and to move with a prescribed velocity. The proposed algorithm is implemented in the open-source software Basilisk and is validated on a number of test cases, such as the Stokes flow between a periodic array of cylinders, vortex decay problem, and multiphase flow around moving solids.

Computational Study of the Dynamics of the Taylor Bubble

“…Here, we describe the governing equations, the initial and boundary conditions, and the numerical method used to solve the equations. The numerical method is based on the algorithm implemented in the open source software Basilisk, and its detailed description is reported in our recent work [31].…”

“…The source terms f σ and f B are the surface tension force (so-called continuum surface force) and a penalization term due to the presence of solids. Their inclusion in the Navier-Stokes equations allows for a volume representation of interfacial effects at fluid-fluid or fluid-solid boundaries [31].…”

“…In our case, the solid is a fixed cylinder so that U s = 0. The penalization coefficient is taken as η = (mh) 2 /ν, where number m = O(1) [31].…”

“…It allows one to simulate multiphase flows with complex topological changes with accurate interface representation. A detailed analysis of the method can be found in [31].…”

“…Our analysis focuses on high-resolution three-dimensional simulations of the Taylor flow. The simulations are carried out using the numerical algorithm we proposed in [31], which is implemented in the open-source software Basilisk [32]. It allows for highly accurate simulations using effective mesh adaptation to resolve all multiscale features of the flow, especially the thin-film flow between the bubble and the wall.…”