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http://dx.doi.org/10.4134/JKMS.j170303

ANALYSIS OF SOME PROJECTION METHODS FOR THE INCOMPRESSIBLE FLUIDS WITH MICROSTRUCTURE  

Jiang, Yao-Lin (School of Mathematics and Statistics Xi'an Jiaotong University)
Yang, Yun-Bo (School of Mathematics and Statistics Xi'an Jiaotong University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 471-506 More about this Journal
Abstract
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;
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