• 대한수학회보
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• 제51권3호
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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.

• 대한수학회지
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• 제61권2호
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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.

• 대한기계학회논문집B
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• 제21권3호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집B
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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.

• 대한기계학회논문집B
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• 제24권6호
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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)

• 한국음향학회지
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• 제31권6호
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• pp.391-398
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• 2012

본 연구에서는 기존의 RANS(Reynolds Averaged Navier Stokes) 방정식을 이용하는 복합 CAA(Computational AeroAcoustics) 방법에 광대역 소음원 생성을 위한 FRPM(Fast Random Particle Mesh) 기법을 적용하여 원심팬 광대역 소음 예측을 수행하였다. 먼저, RANS 방정식을 이용하여 원심팬 주위의 유동장을 예측하여 주요한 소음원 영역을 추론하고, 추론된 소음원 영역에 FRPM 기법을 적용하여 통계적 특성을 만족하는 난류를 재생하였다. RANS 방정식으로부터 해석된 유동장과 FRPM 기법으로부터 재생된 유동장을 이용하여 합성한 유동장에 음향상사법(Acoustic Analogy)을 적용하여 원심팬의 소음원을 생성하였다. 생성된 원심팬의 소음원을 경계요소법(Boundary Element Method)으로 구현된 선형전파모델에 적용하여 원심팬의 광대역 소음을 예측하였다. 원심팬에 대한 소음 측정값과의 비교를 통하여 제안된 기법이 원심팬의 순음 소음 및 광대역 소음 예측에 효과적임을 확인하였다.