An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions

An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions

Year:    2018

Communications in Computational Physics, Vol. 23 (2018), Iss. 3 : pp. 640–664

Abstract

In this paper, an immersed boundary (IB) method for simulating the interfacial flows with insoluble surfactant in three dimensions is developed. We consider a doubly periodic interface separating two fluids where the surfactant exists only along the evolving interface. An equi-arclength parametrization is introduced in order to track the moving interface and maintain good Lagrangian meshes, so stable computations can be performed without remeshing. This surface mesh-control technique is done by adding two artificial tangential velocity components into the Lagrangian marker velocity so that the Lagrangian markers can be equi-arclength distributed during the time evolution. As a result, the surfactant equation on the interface must be modified based on the new parametrization. A conservative scheme for solving the modified surfactant equation has been developed and proved to satisfy the total surfactant mass exactly in discrete level. A series of numerical experiments consisting of the validation of Lagrangian mesh control technique, the convergence study, the study of self-healing dynamics, and the simulations of two-layer fluids under Couette flow have been conducted to test our present numerical scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2017-0090

Communications in Computational Physics, Vol. 23 (2018), Iss. 3 : pp. 640–664

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Insoluble surfactant a conservative scheme mesh control interfacial flow Navier-Stokes flow immersed boundary method.