Browsing by Author "Xu, Jian-Jun"

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A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant
(2014-02-01)
Xu, Jian-Jun
;
Huang, Yunqing
;
Lai, Ming-Chih
;
Li, Zhilin
;
應用數學系
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.
A level-set method for two-phase flows with soluble surfactant
(2018-01-15)
Xu, Jian-Jun
;
Shi, Weidong
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
A level-set method is presented for solving two-phase flows with soluble surfactant. The Navier-Stokes equations are solved along with the bulk surfactant and the interfacial surfactant equations. In particular, the convection-diffusion equation for the bulk surfactant on the irregular moving domain is solved by using a level-set based diffusive-domain method. A conservation law for the total surfactant mass is derived, and a re-scaling procedure for the surfactant concentrations is proposed to compensate for the surfactant mass loss due to numerical diffusion. The whole numerical algorithm is easy for implementation. Several numerical simulations in 2D and 3D show the effects of surfactant solubility on drop dynamics under shear flow. (C) 2017 Elsevier Inc. All rights reserved.