@Article{CiCP-15-451,
author = {Jian-Jun Xu, Yunqing Huang, Ming-Chih Lai and Zhilin Li},
title = {A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant},
journal = {Communications in Computational Physics},
year = {2014},
volume = {15},
number = {2},
pages = {451--469},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.241012.310513a},
url = {http://global-sci.org/intro/article_detail/cicp/7101.html}
}