An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces
Year: 2022
Author: Jin Wang, Xu Zhang, Qiao Zhuang
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 4 : pp. 563–586
Abstract
In this article, we develop 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 in [29]. 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. The numerical results are compared to the analytical solution as well as the standard finite element method with body-fitting meshes. Numerical results indicate the optimal order of convergence of the IFE method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20659
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 4 : pp. 563–586
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Navier-Stokes interface problems nonconforming immersed finite element methods moving interface.