Mathematical Sciences Department
Numerical Methods Seminar
Speaker: Qiao Zhuang, WPI
Thursday, January 12, 2023
11:00 am - 12:00 pm
Stratton Hall 309
Title: An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces
Abstract: In this talk, we introduce a Cartesian-mesh finite element method for solving Navier- Stokes interface problems with moving interfaces. The spatial discretization uses the immersed Crouzeix-Raviart nonconforming finite element introduced by D. Jones and X. Zhang (2021). A backward Euler full-discrete scheme is developed which embeds Newton’s iteration to treat the nonlinear convective term. The proposed IFE method does not require any stabilization terms while maintaining its convergence in optimal order. Numerical experiments with various interface shapes and jump coefficients are provided to demonstrate the accuracy of the proposed method. Numerical results indicate the optimal order of convergence of the IFE method.