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Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations

Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations

Year:    2024

Author:    Xiaowei Bi, Demin Liu

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1519–1548

Abstract

In this paper, the first-order and second-order semi-discrete predictor-multicorrector (PMC) algorithms to solve the 2D/3D unsteady incompressible micropolar fluid equations (IMNSE) are proposed. In the algorithms, the first-order and second-order BDF formulas are adopted to approximate the time derivative terms. At each time step, two elliptical sub-problems with Dirichlet conditions are solved at the prediction step, the strategy of projection about linear momentum equation with additional viscosity term and the elliptical sub-problems about angular momentum are solved at the multicorrection step. Furthermore, the unconditional stability and error estimates of the first-order scheme are proved theoretically. Numerical experiments are carried out to show the effectiveness of the algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0256

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1519–1548

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Micropolar fluid equations predictor-multicorrector algorithm finite element method error estimates.

Author Details

Xiaowei Bi

Demin Liu