• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.25-40
• /
• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2010.11a
• /
• pp.760-763
• /
• 2010

The expansion of 1D numerical code to 2D or 3D is needed in order to improve the analysis accuracy of the interior ballistics. The cut cell method has been imposed for the code expansion to multi dimensions. The MUSCL-Hancock scheme as a high resolution method has been selected. A feasibility of the cut cell method has been verified by analyzing the free piston problem.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.631-638
• /
• 1996

The parabolic free boundary problem with Puschino dynamics is given by (see in [3]) $$ (1) { \upsilon_t = D\upsilon_{xx} - (c_1 + b)\upsilon + c_1 H(x - s(t)) for (x,t) \in \Omega^- \cup \Omega^+, { \upsilon_x(0,t) = 0 = \upsilon_x(1,t) for t > 0, { \upsilon(x,0) = \upsilon_0(x) for 0 \leq x \leq 1, { \tau\frac{dt}{ds} = C)\upsilon(s(t),t)) for t > 0, { s(0) = s_0, 0 < s_0 < 1, $$ where $\upsilon(x,t)$ and $\upsilon_x(x,t)$ are assumed continuous in $\Omega = (0,1) \times (0, \infty)$.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.25 no.5
• /
• pp.439-446
• /
• 2012

This paper presents an implicit moving least squares(MLS) difference method for improving the solution accuracy of 1-D free boundary problems, which implicitly updates the topology change of moving interface. The conventional MLS difference method explicitly updates the moving interface; it requires no iterative solution procedure but results in the loss of accuracy. However, the newly developed implicit scheme makes the total system nonlinear involving iterative solution procedure, but numerical verification show that it dramatically elevates the solution accuracy with moderate computation increase. Through numerical experiments for melting problems having moving singularity, it is verified that the proposed method can achieve the second order accuracy.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.18 no.4
• /
• pp.1-11
• /
• 1981

A flow problem around a ship hull with the nonlinear free surface boundary condition has been considered within the potential flow assumption. The Green's function based on the hull boundary condition is constructed numerically and used to satisfy the free surface boundary condition. This singularity to be distributed ideally on the undulating free surface is put actually, for practical reasons, on the flat water surface with the assumption of linear variation of velocities between the two positions. The surfaces of singularity distribution are approximated by Hess and Smith type quadrilaterals. The radiation condition is only crudely satisfied and this produced one of the major difficulties arising in the present way of attacking the problem.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.389-399
• /
• 1995

We consider the reaction-diffusion system of two-component model in one-dimensional space described by $$ (1) u_s = d_1 u_{xx} + f(u, \upsilon) \upsilon_t = d_2\upsilon_{xx} + \gammag(u, \upsilon) $$ where $d_1$ and $d_2$ are the diffusion rates of u and $\upsilon$, and $\gamma$ is the ration of reaction rates. It is interesting the case of that there are differences in the diffusion and reaction rates of u and $\upsilon$.

• Journal of the Society of Naval Architects of Korea
• /
• v.47 no.1
• /
• pp.1-10
• /
• 2010

In the present paper, a numerical method based on the constraint interpolation profile (CIP) method is applied for simulating two-dimensional violent sloshing problems. The free surface boundary value problem is considered as a multiphase problem which includes water and air. A stationary Cartesian grid system is adopted, and an interface capturing method is used to trace the shape of free surface profile. The CIP combined unified procedure (CCUP) scheme is applied for flow solver, and the tangent of hyperbola for interface capturing (THINC) scheme is used for interface capturing. Numerical simulations have been carried out for partially-filled 2D tanks under forced sway and roll motions at various filling depths and frequencies. The computational results are compared with experiments and/or the other numerical results to validate the present numerical method.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2008.03a
• /
• pp.659-665
• /
• 2008

The 1-D numerical study of the interior ballistics has been conducted. The unsteady compressible 1-D CFD code using SIMPLER algorithm and QUICK scheme has been developed. The mathematical model of the two-phase flow has been established for the behavior of the interior ballistics. The moving boundary due to the projectile motion as the physical phenomena of the interior ballistics results in the varied control volume. In order to analyze the moving boundary, the numerical codes, which apply the ghost-cell extrapolation method and the Lagrangian method respectively, have been developed. The ghost-cell extrapolation method has been used in the Eulerian coordinate system. The Lagrangian method has been used in Non-Eulerian coordinate system. These codes have been verified through the analysis of the free piston motion problem in the tube. Through this study, the basic techniques of the numerical code for the multi-dimensional two-phase flow of the interior ballistics have been obtained.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.53-65
• /
• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.42 no.6
• /
• pp.99-110
• /
• 2005

These days, many image processing techniques have been studied for effective image compression. Among those, The 2D image filtering is widely used for 2D image processing. The 2D image filtering can be implemented by performing the 1D linear filter separately in the horizontal and vertical direction. Efficiency of image compression depends on what filtering method is used. Generally, circular convolution is widely used in 2D image filtering for image processing. However it doesn't consider correlations at the boundary region of image, therefore effective filtering can not be performed. To solve this problem. I proposed new convolution technique using loop convolution which satisfies the 'alias-free' and 'error-free' requirement in the reconstructed image. This method could provide more effective compression performance than former methods because it used highly-correlated data when performed at the boundary region. In this paper, Sub-band Coding(SBC) was adopted to analyze efficiency of proposed filtering technique, and the simulator developed by Java-based language was used to examine the performance of proposed method.