题目：An Augmented Method for Stokes-Darcy FSI Problems & A New FEM-FD method
报告人：Zhilin Li彩票平台-登录彩票平台-登录，Center for Research in Scientific Computation & Mathematics彩票平台-登录， North Carolina State University彩票平台-登录彩票平台-登录，USA
地点：ZOOM Meeting ID: 930 8323 4836彩票平台-登录，Passcode: 535863
摘要：In this talk, a new decoupling method based Cartesian meshes is proposed for a fluid structure interactions between a fluid flow modelled by the Stokes equations and a porous media modelled by the Darcy’s law. Such a model has many applications including oil industry and mathematical biology. The idea is to introduce several interface variables so that the problems can be solved through several Helmholtz/Poisson equations for which a fast Poisson solver can be utilized. The augmented variables that have co-dimensioned one compared with that of the velocity and pressure are chosen so that the BJS conditions are satisfied. Numerical examples are also presented. We have showed the equivalence between the original problem and the transformed one. One interesting question is how to solve the resulted Schur complement system efficiently.
If time allows, I will also present a recent work on anisotropic interface problem using a new finite element-finite difference (FE-FD) method that combines a finite element discretization (away from the interface) whose coefficient matrix is a symmetric semi-positive definite, with a finite difference discretization (near or on the interface) whose coefficient matrix part has properties of an M-matrix.