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A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant

Published online by Cambridge University Press:  03 June 2015

Jian-Jun Xu ,
Yunqing Huang ,
Ming-Chih Lai  and
Zhilin Li
Jian-Jun Xu*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Hunan 410005, China Hunan Key Lab for Computation and Simulation in Science and Engineering, Hunan 410005, China
Yunqing Huang*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Hunan 410005, China Hunan Key Lab for Computation and Simulation in Science and Engineering, Hunan 410005, China
Ming-Chih Lai*
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan
Zhilin Li*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
*
Corresponding author.Email:jjxu21@xtu.edu.cn
Email:huangyq@xtu.edu.en
Email:melai@math.nctu.edu.tw
Email:zhilin@math.ncsu.edu
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Abstract

In this paper, a numerical method is presented for simulating the 3D interfacial flows with insoluble surfactant. The numerical scheme consists of a 3D immersed interface method (IIM) for solving Stokes equations with jumps across the interface and a 3D level-set method for solving the surfactant convection-diffusion equation along a moving and deforming interface. The 3D IIM Poisson solver modifies the one in the literature by assuming that the jump conditions of the solution and the flux are implicitly given at the grid points in a small neighborhood of the interface. This assumption is convenient in conjunction with the level-set techniques. It allows standard Lagrangian interpolation for quantities at the projection points on the interface. The interface jump relations are re-derived accordingly. A novel rotational procedure is given to generate smooth local coordinate systems and make effective interpolation. Numerical examples demonstrate that the IIM Poisson solver and the Stokes solver achieve second-order accuracy. A 3D drop with insoluble surfactant under shear flow is investigated numerically by studying the influences of different physical parameters on the drop deformation.

Keywords

76D0765M063D immersed interface methodlevel-set methodinsoluble surfactantStokes interfacial flowdrop deformation
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 2 , February 2014 , pp. 451 - 469
Copyright
Copyright © Global Science Press Limited 2014

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