Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2017.05.04
  • Accepted : 2017.10.25
  • Published : 2018.03.01
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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.

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References

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