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

作　　者：Jian-Jun Xu Yunqing Huang Ming-Chih Lai Zhilin Li 

机构地区：[1]School of Mathematical and Computational Sciences,Xiangtan University,Hunan 410005,China [2]Department of Applied Mathematics,National Chiao Tung University,Hsinchu 30050,Taiwan [3]Department of Mathematics,North Carolina State University,Raleigh,NC,27695,USA [4].4 Hunan Key Lab for Computation and Simulation in Science and Engineering,Hunan 410005,China [5]School of Mathematical Sciences,Nanjing Normal University,Nanjing,China.

出　　处：《Communications in Computational Physics》2014年第2期451-469,共19页计算物理通讯（英文）

基　　金：supports by Hunan Provincial Education Department(10C1264),Xiangtan Univ.(10QDZ45),and Hunan NSFC(10JJ70);supported in part by NSFC key project 11031006;supported in part by National Science Council of Taiwan under grant NSC98-2115-M-009-014-MY3 and NCTS.Z.Li was supported in part by the US ARO grant 550694-MA,the AFSOR grant FA9550-09-1-0520,the US NSF grant DMS-0911434,the NIH grant 096195-01,and CNSF11071123.

摘　　要：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.

关 键 词：Multigrid method constrained Cauchy-Born elasticity NANOINDENTATION CauchyBorn rule. 

分 类 号：O17[理学—数学]