Adv. Appl. Math. Mech., 16 (2024), pp. 1519-1548.
Published online: 2024-10
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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} }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.