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Volume 16, Issue 6
Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations

Xiaowei Bi & Demin Liu

Adv. Appl. Math. Mech., 16 (2024), pp. 1519-1548.

Published online: 2024-10

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  • 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.

  • AMS Subject Headings

76M10, 65N12, 65N30

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COPYRIGHT: © Global Science Press

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@Article{AAMM-16-1519, author = {Bi , Xiaowei and Liu , Demin}, title = {Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0256}, url = {http://global-sci.org/intro/article_detail/aamm/23477.html} }
TY - JOUR T1 - Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations AU - Bi , Xiaowei AU - Liu , Demin JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1519 EP - 1548 PY - 2024 DA - 2024/10 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2022-0256 UR - https://global-sci.org/intro/article_detail/aamm/23477.html KW - Micropolar fluid equations, predictor-multicorrector algorithm, finite element method, error estimates. AB -

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.

Bi , Xiaowei and Liu , Demin. (2024). Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations. Advances in Applied Mathematics and Mechanics. 16 (6). 1519-1548. doi:10.4208/aamm.OA-2022-0256
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