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 jum...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.展开更多
We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid operator.This method accelerates the relaxation...We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid operator.This method accelerates the relaxation process and considerably reduces the computational cost.In particular,it saves quite a bit when dislocations nucleate and move,as demonstrated by the simulation results.展开更多
基金supports by Hunan Provincial Education Department(10C1264),Xiangtan Univ.(10QDZ45),and Hunan NSFC(10JJ70)supported in part by NSFC key project 11031006supported 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.
文摘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.
基金supported by National Science Foundation grant DMS-1217315supported by National Natural Science Foundation of China under the grant 10932011,91230203 and by the funds for creative research group of China(Grant No.11021101)+1 种基金by the support of CAS National Center for Mathematics and Interdisciplinary Sciencessupported by National Natural Science Foundation of China under the grants 11001210 and 11171305 and 91230203.
文摘We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid operator.This method accelerates the relaxation process and considerably reduces the computational cost.In particular,it saves quite a bit when dislocations nucleate and move,as demonstrated by the simulation results.
