• 충청수학회지
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• 제28권1호
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• pp.151-159
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• 2015

This paper investigates temporal regularity of solutions for the incompressible Euler equations in a critical Besov space $B^{\frac{d}{p}+1}_{p,1}(\mathbb{R}^d)$ for $1{\leq}p{\leq}d$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.243-248
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• 2012

We consider the (possible) finite time blow-up of the smooth solutions of the 3D incompressible Euler equations in a smooth domain or in $R^3$. We derive blow-up criteria in terms of $L^{\infty}$ of the partial component of Hessian of the pressure together with partial component of the vorticity.

• 대한수학회지
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• 제32권1호
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• pp.41-50
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• 1995

• 충청수학회지
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• 제31권4호
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• pp.363-368
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• 2018

The aim of this work is to derive a partial differential equation that explains the movement of vortex lines on a vortex trajectory surface in a three dimensional incompressible inviscid flow.

• 대한수학회지
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• 제55권1호
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• pp.211-224
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• 2018

We consider a certain three dimensional Euler flow with infinite energy, which is sometimes called the columnar or two and half dimensional flow. We prove the global smoothness of such flow in ${\mathbb{R}}^3$ when the initial data is in some Sobolev or Besov spaces and ${\partial}_3u_3$ is nonnegative.

• 대한수학회보
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• 제55권3호
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• pp.881-898
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• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• 한국전산유체공학회지
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• 제2권1호
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• pp.8-12
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• 1997

The three-dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for three contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreement.

• 대한조선학회논문집
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• 제31권1호
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• pp.63-70
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• 1994

항공유체의 계산에 주로 사용되는 음해법의 하나인 IAF(Implicit Approximate Factorization)법을 이용해 3차원 Wigley 선형 주위의 자유표면파 및 점성유동장을 해석하였다. IAF 법을 사용함으로서 기존 Euler 양해법의 계산 시간을 50% 이상 감소시키는데 성공하였다. 수치기법으로 국부선형화와 Euler 음해법을 사용하였으며 artificial viscosity의 생성을 위한 압력 구배항은 사용하지 않았다. 수치 계산은 Reynolds 수 $10^6$. Froude 수 0.25, 0.289 및 0.316에 대하여 수행하였고 난류 모형으로는 Baldwin-Lomax 모형을 사용하였으며 주요 계산 결과로는 자유표면화 형상 및 속도분포 등이었다. 본 연구에서는 그 중에서 자유표면파 형상에 대한 계산 결과를 실험값 및 Euler 양해법을 사용한 결과와 각각 비교 검토하였다.

• 대한수학회지
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• 제31권3호
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• pp.367-373
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• 1994

Let us consider the Cauchy problem $$ {\rho_t + \upsilon \cdot \nabla\rho = 0 {\rho[\upsilon_t + (\upsilon \cdot \nabla)\upsilon] + \nabla p + \rho f {div \upsilon = 0 (1.1) {\rho$\mid$_t = 0 = \rho_0(x) {\upsilon$\mid$_t = 0 = \upsilon_0(x) $$ in $Q_T = R^3 \times [0,T]$, where $f(x,t), \rho_0(x) and \upsilon_0(x)$ are given, while the density $\rho(x,t)$, the velocity vector $\upsilon(x,t) = (\upsilon^1(x,t),\upsilon^2(x,t),\upsilon^3(x,t))$ and the pressure p(x,t) are unknowns. The equations $(1.1)_1 - (1.1)_3$ describe the motion of a nonhomogeneous ideal incompressible fluid.

• 대한조선학회논문집
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• 제41권4호
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• pp.17-29
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• 2004

Internal waves are computed using a ghost fluid method on an unstructured grid. Discontinuities in density and dynamic pressure are captured in one cell without smearing or oscillations along a multimaterial interface. A time-accurate incompressible Navier-Stokes/Euler solver is developed based on a three-point backward difference formula for the physical time marching. Artificial compressibility is introduced with respect to pseudotime and an implicit method is used for the pseudotime iteration. To track evolution of an interface, a level set function is coupled with the governing equations. Roe's flux difference splitting method is used to calculate numerical fluxes of the coupled equations. To get higher order accuracy, dependent variables are reconstructed based on gradients which are calculated using Gauss theorem. For each edge crossing an interface, dynamic pressure is assigned for a ghost node to enforce the continuity of total pressure along the interface. Solitary internal waves are computed and the results are compared with other computational and experimental results.