대한수학회지 (Journal of the Korean Mathematical Society)

  • 제55권2호
  • /
  • Pages.471-506
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  • 2018
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2017.05.04
  • 심사 : 2017.10.25
  • 발행 : 2018.03.01
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초록

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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참고문헌

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