• Journal of computational fluids engineering
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• v.16 no.4
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• pp.72-83
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• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.269-277
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• 2014

A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.746-752
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• 2001

Design sensitivity analysis for nonlinear structural problems has been emerged in the last decade as a glowing area of engineering research. As a result, theoretical formulations and computational algorithms have already developed for design sensitivity of nonlinear structural problems. There is not enough research for practical nonlinear problems using multi-element, due to difficulties of implementation into FEA. Therefore, nonlinear response analysis for stiffened shell which consists of Mindlin plate and Timoshenko beam, was considered. Specially, it presents the backward-Euler method which is adopted to describe an exact yield state in the stress computation procedure. Then, design sensitivity analysis of nonlinear structures, particularly elasto-perfectly-plastic structure, is developed using direct differentiation method. The accuracy of the developed sensitivity analysis was compared with the central finite difference method. Finally, on the basis of above results, design improvement for stiffened shell is suggested.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.252-254
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• 2006

The recent improvement in the performance of digital processor, the application of control technology, which used in the HVDC(High Voltage Direct Current) system with the digital processors, has increased. Having this research development as the basis, this paper presents an achievement of progression by tuning the parameter of PI controller based on Genetic Algorithms(GAs) and by controlling with PI controller with a developed simulator by applying the Matrix operating function, voltage source switching element, modified nodal analysis which can include transformer and the backward Euler which does not create the problem of numerical oscillation. As a result, I expect this development in the simulator HVDC System to bring more application in the field of control technology research with an expanded practicality.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.3
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• pp.110-117
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• 1998

A continuum-based configuration design sensitivity analysis method is developed for kinematically driven mechanical systems. The configuration design variable for mechanical systems is defined. The 3-1-3 Euler angle is employed as the orientation design variable. Kinematic admissibility conditions of configuration design change. Direct differentiation method is used to derive the governing equations of the design sensitivity. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.4
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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.

• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.98-105
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• 1999

The Pressure-based Unstructured-grid Navier-Stokes Solver PUNS-2/3D for incompressible steady and unsteady viscous flows has been developed. It is based on nonstaggered cell-centered finite volume method. Second-order upwind scheme with least-square reconstruction is used for convective fluxes. The SIMPLE method is implemented to couple the pressure and velocity fields. And the time derivatives in the momentum equations are discretised using a second-order Euler backward-differencing scheme. The discretised linear equations are solved by the preconditioned Biconjugate Gradient Stabilized method(Bi-CGSTAB). The developed solver is applied to validation problems using hybrid meshes.

• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.90-97
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• 1999

An implicit turbulent flow solver is developed for 2-D unstructured hybrid meshes. Spatial discretization is accomplished by a cell-centered finite volume formulation using an upwind flux differencing. Time is advanced by an implicit backward Euler time stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one equation model, which is coupled with wall function. The numerical method is applied for flows on a flat plate, the NACA 0012 airfoil, and the Douglas 3 element airfoil. The results are compared with experimental data.