A Linearized, Decoupled and Unconditionally Stable BDF2 FEM for the Active Fluid Model
Year: 2025
Author: Yuxing Zhang, Bo Wang
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 1 : pp. 40–70
Abstract
In this paper, we develop a linear and decoupled fully discrete mixed finite element scheme for the active fluid model. The scheme employs an auxiliary variable to reformulate the fourth-order derivative term, an implicit-explicit treatment to deal with the nonlinear terms and the second-order pressure-projection method to split the velocity and pressure. Through rigorous theoretical analysis, the unique solvability, unconditional stability and error estimates of the numerical scheme are obtained. Then, several numerical experiments are presented to verify the efficiency and accuracy of the proposed scheme. Finally, the comparison of simulation results with laboratory results, including the motion direction of active fluid changes from disorder to order and reversal in 2D and 3D, demonstrate that the scheme can accurately capture and handle the complex dynamics of active fluid motion.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1003
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 1 : pp. 40–70
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Active fluid error estimates auxiliary variable BDF2 pressure-projection.
Author Details
Yuxing Zhang Email
Bo Wang Email