• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.847-862
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• 2014

Finite element approximation solutions of the optimal control problems for stochastic Stokes equations with the forcing term perturbed by white noise are considered. Error estimates are established for the fully coupled optimality system using Brezzi-Rappaz-Raviart theory. Numerical examples are also presented to examine our theoretical results.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.227-253
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• 2024

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space BCL_-∞(H). We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.350-357
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• 1997

The transient incompressible flow behind the axisymmetric bluff body is numerically simulated using the random vortex method(RVM). Based on the vorticity formulation of the unsteady Navier-Stokes equations, the Lagrangian approach with a stochastic simulation of diffusion using random walk technique is employed to account for the transport processes of the vortex elements. The numerical solutions for 2-dimensional recirculating flow behind a backward-facing step in the laminar range of Reynolds number are compared with experimental data. The present simulation focuses on the transitional flow regime where the recirculation zone behind the bluff body becomes highly unsteady and large-scale vortex eddies are shed from the bluff body wake due to intrinsic shear layer instabilities. The unsteady vertical flow structures and the mixing characteristics behind the bluff body are discussed in detail.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.625-630
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• 2000

Numerical and experimental investigations are peformed for the rarefied gas flows in pumping channels of a helical-type drag pump. Modern turbomolecular pumps include a drag stage in the discharge side, operating roughly in $10^{-2}{\sim}10Torr$. The flow occurring in the pumping channel develops from the molecular transition to slip flow traveling downstream. Two different numerical methods are used in this analysis: the first one is a continuum approach in solving the Navier-Stokes equations with slip boundary conditions, and the second one is a stochastic particle approach through the use of the direct simulation Monte Carlo(DSMC) method. The flow in a pumping channel is three-dimensional(3D), and the main difficulty in modeling a 3D case comes from the rotating frame of reference. Thus, trajectories of particles are no longer straight lines. In the Present DSMC method, trajectories of particles are calculated by integrating a system of differential equations including the Coriolis and centrifugal forces. Our study is the first instance to analyze the rarefied gas flows in rotating frame in the presence of noninertial effects.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.6
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• pp.860-869
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• 2000

Numerical and experimental investigations are performed for the molecular transition and slip flows in pumping channels of a disk-type drag pump. The flow occurring in the pumping channel develops from the molecular transition to the slip flow traveling downstream. Two different numerical methods are used in this analysis: the first one is a continuum approach in solving the Navier-Stokes equations with slip boundary conditions, and the second one is a stochastic approach through the use of the direct simulation Monte Carlo method. In the experimental study, the inlet pressures are measured for various outlet pressures in the range of 0.1{\sim}4Torr. From the present study, the numerical results of predicting the performance, obtained by both methods, agree well with the experimental data for the range of Knudsen number $Kn{\leq}0.1$ (i.e., the slip flow regime). But the results from the second method only agree with the experimental data for Kn>0.1(i.e., the molecular transition regime)

• The Journal of the Acoustical Society of Korea
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• v.31 no.6
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• pp.391-398
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• 2012

In this paper, prediction of centrifugal fan was conducted through combination the hybrid CAA method which was used to predict the fan noise with the FRPM technique which was used to generate the broadband noise source. Firstly, flow field surround the centrifugal fan was computed using the RANS equations and noise source region was deducted from the computed flow field. Then the FRPM technique was applied to the source region for generation of turbulence which satisfies the stochastic features. The noise source of the centrifugal fan was modeled by applying the acoustic analogy to the synthesized flow field from the computed and generated flow fields. Finally, the broadband noise of the centrifugal fan was predicted through combination the modeled noise source with the linear propagation which was realized using the boundary element method. It was confirmed that the proposed technique is efficient to predict the tonal and broadband noises of centrifugal fan through comparison with the measured data.