J. Korean Math. Soc. 2018; 55(2): 471-506
Online first article December 6, 2017 Printed March 1, 2018
https://doi.org/10.4134/JKMS.j170303
Copyright © The Korean Mathematical Society.
Yao-Lin Jiang, Yun-Bo Yang
Xi'an Jiaotong University, Xi'an Jiaotong University
In this article, some projection methods (or fractional-step methods) are proposed and analyzed for the micropolar Navier-Stokes equations (MNSE). These methods allow us to decouple the MNSE system into two sub-problems at each timestep, one is the linear and angular velocities system, the other is the pressure system. Both first-order and second-order projection methods are considered. For the classical first-order projection scheme, the stability and error estimates for the linear and angular velocities and the pressure are established rigorously. In addition, a modified first-order projection scheme which leads to some improved error estimates is also proposed and analyzed. We also present the second-order projection method which is unconditionally stable. Ample numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the methods.
Keywords: micropolar Navier-Stokes, projection method, error estimates, decouple method, fluids with microstructure
MSC numbers: 65N15, 65N30, 65N12, 65M12
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