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报告题目：A Least Squares Augmented Method for Fluid and Porous Media Couplings

报告人：Zhilin Li（North Carolina State University）

时间：2017年1月3日下午14:10

地点：船海楼15楼大会议室

主办单位：科学技术研究院

承办单位：船舶工程学院

报告人简介：

(a) Professional Preparation

ØNanking Normal University Mathematics B.S. 1982

ØNanking Normal University Mathematics M.S. 1988

ØUniversity of Washington Applied Mathematics M.S. 1991

ØUniversity of Washington Applied Mathematics Ph.D. 1994

(b) Appointments

Ø1997- Assistant, Associate, Full Professor, Mathematics Department, North Carolina State University

Ø1996-7 Assistant Professor, Mathematics, Mississippi State University

Ø1994-6 CAM (Computational and Applied Mathematics) Assistant Professor, Mathematics

ØDepartment, University of California at Los Angeles (UCLA)

Total publications as of October 31, 2016: 127.

(c) Research Grants Current and past: NSF, NIH, NSF/NIGMS, ARO, AFOSR, Oak Ridge, DOE/ARO etc.

(d) Synergistic Activities

ØCo-invented the Immersed Interface Method (IIM) and Augmented Immersed Interface Method. The published monograph in SIAM Frontiers provides a good reference for researchers and graduate students.

ØChair of the organizing committee of the “International Workshop on Fluid Structure Interaction Problems”, IMS, National University of Singapore, May 30-June 4, 2016, and sequences of the series; one SAMSI annual program; programs in Banff, Fields Institute, IPAM etc.

ØEditor of several special issues of including AMS Contemporary Mathematics, CiCP.

ØAssociated editor for 5 journals.

报告简介:

Simulations of fluid and porous media couplings are important and challenging because of different governing equations and complicated interface conditions such as BJ and BJS relations. Most of numerical methods in the literature are based on finite element formulations in which the interface conditions are incorporated in the variational forms. One consequence is that the large errors across the interface due to low regularity of the solution if the mesh is not aligned with the interface. The large discrete system makes harder to use fast solvers.

In this talk, we propose a finite difference approach with unfitted meshes. By introducing several augmented variables along the interface, we can decouple the original problem as several Poisson/Helmholtz equations with intermediate jump conditions in the solution and the normal derivatives. One obvious advantage is that a fast Poisson/Helmholtz solver can be utilized. The augmented variables should be chosen such that the Beavers-Joseph-Saffman (BJS) and other interface conditions are satisfied. Another significant strategy is to enforce the divergence condition at the interface from the fluid side. We have shown that the original and transformed systems are equivalent. Because the interface conditions are enforced in strong form, we have observed second order convergence for both of the velocity and the pressure for our constructed non-trivial analytic solutions with circular interfaces. The proposed new method has also been utilized to simulate different flow/porous media setting with complicated interfaces which leads to some interesting simulations results such as effect of corners, orientation effect etc.