An efficient and unconditionally stable finite element scheme for an active magnetic fluid model

Yuxing Zhang, Bo Wang, Qiang Wang and Jian Li

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 447-463

Abstract: In this article, based on the laws of mass and momentum conservation and the coupled effects of electromagnetism and hydrodynamics, we derive an active magnetic fluid model to qualitatively describe the collective and organized motion of magnetotactic bacteria at high concentrations. To solve the developed model, we construct a decoupled, linear and unconditionally stable finite element scheme by employing an auxiliary variable, the implicit-explicit approach and the pressure projection method. The numerical scheme has three distinct properties: (i) the velocity field can be approximated by lower order finite element; (ii) the velocity and magnetic fields are decoupled by adding a stabilization term; (iii) the velocity and pressure are split using the pressure projection method. We also prove the unique solvability and unconditional stability of the proposed scheme. Numerical examples are presented to validate the theoretical results. Comparisons between simulation and laboratory results demonstrate that the active magnetic fluid model can accurately capture the complex dynamics of active magnetic fluid motion.

Keywords: Active magnetic fluid; Pressure-projection method; Auxiliary variable; Unique solvability; Unconditional stability (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475426000637
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:447-463

DOI: 10.1016/j.matcom.2026.02.017

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().