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Volume 19, Issue 4
An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces

Jin Wang, Xu Zhang & Qiao Zhuang

Int. J. Numer. Anal. Mod., 19 (2022), pp. 563-586.

Published online: 2022-06

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  • 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.

  • Keywords

Navier-Stokes, interface problems, nonconforming immersed finite element methods, moving interface.

  • AMS Subject Headings

35R05, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-563, author = {Jin and Wang and and 23782 and and Jin Wang and Xu and Zhang and and 23783 and and Xu Zhang and Qiao and Zhuang and and 23784 and and Qiao Zhuang}, title = {An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20659.html} }
TY - JOUR T1 - An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces AU - Wang , Jin AU - Zhang , Xu AU - Zhuang , Qiao JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 563 EP - 586 PY - 2022 DA - 2022/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20659.html KW - Navier-Stokes, interface problems, nonconforming immersed finite element methods, moving interface. AB -

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.

Jin Wang, Xu Zhang & Qiao Zhuang. (2022). An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Equations with Moving Interfaces. International Journal of Numerical Analysis and Modeling. 19 (4). 563-586. doi:
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