Mathematical Sciences Department, Numerical Methods Seminar - Qiao Zhuang, WPI "An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces" SH309

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Location
Floor/Room #
309
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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.

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