An Efficient Rotational Pressure-Correction Scheme for the 2D/3D Navier-Stokes/Darcy Coupling Problem
Year: 2024
Author: Minting Zhao, Jiawei Gao, Md. Abdullah Al Mahbub, Dan Chen
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 6 : pp. 850–878
Abstract
This article proposes and analyzes a rotational pressure-correction method for the Navier-Stokes/Darcy (NSD) system with Beavers-Joseph-Saffman-Jones interface conditions. This method mainly solves the Navier-Stokes/Darcy problem in two steps. The first step is the viscous step. The intermediate velocity can be obtained after the pressure gradient is explicitly processed by the algorithm. The second step is the projection step, which first projects the intermediate velocity onto a divergence-free space, and then corrects the velocity and pressure. The main advantage of these methods is that they have first/second order accuracy and do not have the incompressibility constraint of NSD system. For solving the Navier-Stokes equations, each time step requires only one vector-valued elliptic equation and one scalar-valued Poisson equation. Therefore, this method has high computational efficiency. Compared with other traditional related methods, this method is no longer affected by any artificial boundary conditions, and can achieve the optimal convergence order. Finally, unconditional stability and long time stability are established. 2D/3D numerical experiments are presented to illustrate the features of the proposed method and verify the results of the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1034
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 6 : pp. 850–878
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: First-order/second-order temporal scheme rotational pressure-correction scheme Navier-Stokes/Darcy system stability 2D/3D numerical experiments.
Author Details
Minting Zhao Email
Jiawei Gao Email
Md. Abdullah Al Mahbub Email
Dan Chen Email