Volume 23, Issue 3
An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions

Yunchang Seol, Shih-Hsuan Hsu & Ming-Chih Lai

Commun. Comput. Phys., 23 (2018), pp. 640-664.

Published online: 2018-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35Q35, 65M06, 76D45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-640, author = {}, title = {An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0090}, url = {http://global-sci.org/intro/article_detail/cicp/10542.html} }
TY - JOUR T1 - An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions JO - Communications in Computational Physics VL - 3 SP - 640 EP - 664 PY - 2018 DA - 2018/03 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0090 UR - https://global-sci.org/intro/article_detail/cicp/10542.html KW - Insoluble surfactant, a conservative scheme, mesh control, interfacial flow, Navier-Stokes flow, immersed boundary method. AB -

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.

Yunchang Seol, Shih-Hsuan Hsu & Ming-Chih Lai. (2020). An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions. Communications in Computational Physics. 23 (3). 640-664. doi:10.4208/cicp.OA-2017-0090
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