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 - <p style="text-align: justify;">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.</p>