• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권4호
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• pp.203-214
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• 2017

In this paper we propose and analyze two a posteriori error estimators for the stabilized $P_1/P_1$ finite element discretization of the Stokes equations. These error estimators are computed by solving local Poisson or Stokes problems on elements of the underlying triangulation. We establish their asymptotic exactness with respect to the velocity error under certain conditions on the triangulation and the regularity of the exact solution.

• 대한수학회지
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• 제46권5호
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• pp.1041-1069
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• 2009

We study the periodic homogenization of the non-stationary Stokes equations. The fundamental homogenization theorem and corrector theorem are proved under a very general assumption on the viscosity coefficients and data. The proofs are based on a weak formulation suitable for an application of classical Tartar's method of oscillating test functions. Such a weak formulation is derived by adapting an argument in Teman's book [Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984].

• 충청수학회지
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• 제35권4호
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• pp.307-313
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• 2022

In this paper, we will consider the periodic stationary Stokes equations on Rⁿ. For the cube of the period, we set Ω = ∏ⁿ_i=1(0, L_i). And we will study the stability of the solutions on various functional spaces, for the Stokes equations on Rⁿ.

• 대한기계학회논문집B
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• 제41권4호
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• pp.239-248
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• 2017

원형 실린더 주위의 유동에 부유된 입자가 실린더 근처에서 분산되거나 실린더에 부착되는 특성을 이해하는 것이 중요하다. 본 연구에서는 입자의 부착을 조절하는 방안으로 실린더의 회전을 고려해 보았고, 실린더의 회전 속도 및 입자의 Stokes 수가 실린더 주위의 유동과 입자의 분산 및 부착 특성에 미치는 영향을 수치해석적으로 연구하였다. 해석 결과 4보다 작은 Stokes 수에서는 회전속도가 증가함에 따라 부착효율이 크게 감소하였고, 4보다 큰 Stokes 수에서는 회전속도가 증가함에 따라 부착효율이 다소 증가하였다. 한편, 회전속도가 일정한 경우에는 Stokes 수가 증가함에 따라 입자의 부착효율이 증가하고, 입자의 부착 위치도 넓어졌다.

• 한국해안·해양공학회논문집
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• 제31권2호
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• pp.41-49
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• 2019

1개층 Boussinesq 방정식(Vu 등, 2018)과 2개층 Boussinesq 방정식(Huynh 등, 2017)을 사용하여 투수방파제를 지나는 cnoid 파의 월파고를 구하였다. 수치실험을 통해 천단고가 낮은 투수방파제를 지나는 cnoid 파의 월파고(Navier-Stokes 방정식으로 구함)가 천단고가 높은 투수방파제를 지나는 통과파고(1개층 Boussinesq 방정식으로 구함)보다 더 작고, 천단고가 해저에 있는 투수방파제를 지나는 통과파고(2개층 Boussinesq 방정식으로 구함)보다 더 크다는 것을 확인하였다. cnoid 파의 파고가 낮을수록 또는 투수방파제의 폭이 좁을수록 1개층 및 2개층 Boussinesq 방정식으로 구한 통과파고가 Navier-Stokes 방정식으로 구한 월파고에 근접한 것을 확인하였다.

• 대한조선학회논문집
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• 제59권2호
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• pp.64-71
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• 2022

In this paper, we simulate the collision of a solitary wave on a vertical wall in a uniform water channel and investigate the effect of damping on the amplitude attenuation. In order to take into account the damping effect, we introduce the Stokes damping whose dissipation is dependent on the velocity of wave motion on the surface of a thin layer of oil. That is, we use the improved Boussinesq equation with Stokes damping to describe the damped wave motion. Our work mainly focuses on the amplitude attenuation of a propagating solitary wave, which may depend on the Stokes damping together with the initial position and initial amplitude of the wave. We utilize the method of images and a powerful numerical tool (functional iteration method) for solving the improved Boussinesq equation, yielding an effective numerical simulation. This enables us to find the amplitudes of the incident wave and reflected one, whose ratio is a measure of the (wave) amplitude attenuation. Accordingly, we have shown that the reflection of a solitary wave by a vertical wall is dependent on not only the initial amplitude and position of a solitary but the Stokes damping.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.1-19
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• 1998

A Chebyshev pseudospectral-finite element method is proposed for two-dimensional unsteady Navier-Stokes equation. The generalized stability and the convergence are proved strictly. The numerical results show the advantages of this method.

• 대한수학회지
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• 제49권6호
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• pp.1163-1174
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• 2012

This paper examines a temperature dependent Stokes flow in a semi-infinite cylinder. Under appropriate initial and boundary conditions the author establishes exponential decay of solutions in energy norm with distance from the finite end of the cylinder.

• 대한수학회논문집
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• 제35권1호
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• pp.339-345
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• 2020

This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.

• 대한수학회논문집
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• 제14권4호
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• pp.833-842
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• 1999

In this paper, we construct a fully discrete solution of the incompressible Navier Stokes equations using implicit Runge kutta method. We prove the existence of the fully discrete solution.