• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.471-506
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• 2018

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.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.3282-3285
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• 1999

Fluid characteristics at microscale were tried to be solved in this paper by showing how they deviate with conventional flow governing equations. (e.g. Navier-Stokes Equation) In earlier studies, this deviation phenomena was caused because of omitting no slip flow condition, micropolar effect and EDL(Electric Double Layer)effect of fluid which are usually negligible at macroscaled phenomena. The characteristics of fluid flow were tried to be studied by measuring pressure difference of specified length of the channels using the almost squared micromachined channels. By acquiring pressure difference, we could drive different values (viscosity, flow velocity. etc) from it and these data will be compared with macroscaled flow characteristics. As making microchannel is not easy work and that our knowledge is at mere stage, we had to fail to make it in this time. The hardest thing in this work is to make a hole which is directly connected with channel. The more efficient and easy way of making microchannel is proposed in this paper.