Xu Zhang, Associate Professor, Department of Mathematics, Oklahoma State University

Xianmin Xu, Professor

Solving Navier-Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes

10:00-11:00 June 29 (Thursday), Tencent Meeting: 876-568-743

In this talk, we introduce a high-order immersed finite element (IFE) method for solving two-phase incompressible Navier-Stokes equation on interface-unfitted meshes. In spatial discretization, we use the newly developed immersed P2-P1 Taylor-Hood finite element. An enhanced partially penalized IFE method which includes the penalization on both interface edges and the interface itself. Ghost penalties are also added for pressure robustness. In temporal discretization, theta-schemes and backward differentiation formulas are adopted. Newton's method is used to handle the nonlinear advection. The proposed method completely circumvents re-meshing in tackling moving-interface problems. Thanks to the isomorphism of our IFE spaces with the standard finite element spaces, the new method enables efficient updates of global matrices, which significantly reduces the over-all computational cost. Comprehensive numerical experiments show that the proposed method is third-order convergent for velocity and second order for pressure in both stationary and moving interface cases.

Bio: Xu Zhang is an Associate Professor in the Department of Mathematics at Oklahoma State University. He received his B.S. degree (2005) and M.S. degree (2008) in Computational Mathematics from Sichuan University, and his Ph.D. degree (2013) in Mathematics from Virginia Tech. He did postdoc training at Purdue University during 2013-2016. Before joining OSU, he was an Assistant Professor at Mississippi State University during 2016-2019. His research is on numerical methods for partial differential equations. Recently, his research focused on immersed finite element methods for PDE interface problems including algorithm development, implementation, error analysis, and engineering applications. Prof. Zhang has received three research grants from National Science Foundation as PI, and the Ralph E. Powe Junior Faculty Enhancement Award from ORAU in 2021. He has authored over 30 journal articles published in SINUM, SISC, JCP, CMAME, JSC, etc., and has been cited more than 1000 times, according to Google Scholar.