• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.449-465
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• 1994

The two common numerical methods to approximate the solution of partial differential equations are the finite element method and the finite difference method. They both lead to solving large sparse linear systems. For many applications, it is not unusal that the order of matrix is greater than 10, 000. For this kind of problem, a direct method such as Gaussian elimination can not be used because of the prohibitive cost. To this end, many iterative methods with modest cost have been studied and proposed by numerical analysts.(omitted)

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1752-1756
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• 2008

A simple, accurate and efficient mesh generation technique, the cut-cell method, is able to represent an arbitrarily complex geometry. Both structured and unstructured grid meshes are used in this method. First, the numerical domain is constructed with regular Cartesian grids as a background grid and then the solid boundaries or bodies are cut out of the background Cartesian grids. As a result, some boundary cells can be contained two numerical conditions such as the flow and solid conditions, where the special treatment is needed to simulate such physical characteristics. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. Also, the TVD-WAF method is applied on the Cartesian cut-cell grids to stabilize numerical results. Present method is validated for the rectangular dam break problems. Initially, a conventional grid is constructed with the Cartesian regular mesh only and then applied to the dam-break flow simulation. As a comparative simulation, a cut-cell grids are applied to represent the flow domain rotated with arbitrary angles. Numerical results from this study are compared with the results from the case of the Cartesian regular mesh only. A good agreement is achieved with other numerical results presented in the literature.

• Journal of Ocean Engineering and Technology
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• v.37 no.5
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• pp.215-224
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• 2023

While melting glaciers due to global warming have facilitated the development of polar routes, Arctic vessels require reliable anti-icing methods to prevent hull icing. Currently, the existing anti-icing method, i.e., the heating coil method, has disadvantages, such as disconnection and power inefficiency. Therefore, a carbon nanotube-based surface heating element method was developed to address these limitations. In this study, the numerical analysis of the surface heating element method was performed using ANSYS. The numerical analysis included conjugate heat transfer and computational fluid dynamics to consider the conduction solids and the effects of wind speed and temperature in cold environments. The numerical analysis method of the surface heating element method was validated by comparing the experimental results of the heating coil method with the numerical analysis results (under the -30 ℃ conditions). The surface heating element method demonstrated significantly higher efficiency, ranging from 56.65-80.17%, depending on the conditions compared to the heating coil method. Moreover, even under extreme environmental conditions (-45 ℃), the surface heating element method satisfied anti-icing requirements. The surface heating element method is more efficient and economical than the heating coil method. However, proper heat flux calculation for environmental conditions is required to prevent excessive design.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.30-40
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• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.488-493
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• 2001

This paper introduces some useful Java technologies for utilizing the Internet in numerical analysis, and suggests one architecture performing efficient numerical analysis in the Intranet by using them. The present work has verified it's possibility by implementing some parts of this architecture with two easy examples. One is based on Servlet-Applet communication, JDBC and Swing. The other is adding multi-threads, file transfer and Java Remote Method Invocation to the former. Through this work it has been intended to make the base for the later advanced and practical research that will include efficiency estimates of this architecture and deal with advanced load balancing.

• Journal of Soil and Groundwater Environment
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• v.11 no.1
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• pp.37-44
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• 2006

This study summarizes advantages and disadvantages of numerical methods and compares ELLAM and LEZOOMPC to develop an efficient numerical modeling technique on contaminant transport. Eulerian-Lagrangian method and Eulerian method are commonly used numerical techniques. However Eulerian-Lagrangian method does not conserve mass globally and fails to treat boundary in a straightforward manner. Also, Eulerian method has restrictions on the size of Courant number and mesh Peclet number because of time truncation error. ELLAM (Eulerian Lagrangian Localized Adjoint Method) which has been popularly used for past 10 years in numerical modeling, is known for overcoming these numerical problems of Eulerian-Lagrangian method and Eulerian method. However, this study investigates advantages and disadvantages of ELLAM and suggests a change for the better. To figure out the disadvantages of ELLAM, the results of ELLAM, LEZOOMPC (Lagrangian-Eulerian ZOOMing Peak and valley Capturing), and visual MODFLOW are compared for four examples having different mesh Peclet numbers. The result of ELLAM generates numerical oscillation at infinite of mesh Peclet number, but that of LEZOOMPC yields accurate simulations. The simulation results suggest that the numerical error of ELLAM could be alleviated by adopting some schemes in LEZOOMPC. In other words, the numerical model which combines ELLAM with backward particle tracking, forward particle tracking, adaptively local zooming, and peak/valley capturing of LEZOOMPC can be developed for not only overcoming the numerical error of ELLAM, but also keeping the numerical advantage of ELLAM.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.923-926
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• 1992

ARMA fast Transversal filter(FTF) algorithm solves the extended least squres estimation problems in a very efficient way. But unfortunately, it exhibits a very unstable behavior, due to the accumulation of round-off errors. So, in this paper, two effective method to stabilize ARMA FTF algorithm is proposed. They are based on the analysis of the propagation of the numerical errors according to a first order linear model. The proposed methods modify the numerical properties of the variables responsible for the numerical instability, while proeserving the theoretical form of the algorithm. The proposed algorithms still have the nice complexity properties of the original algorithm, but have a much more stable brhavior.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.725-728
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• 2005

The scattering problem of the randomly rough surface is examined by the method of moments(MoM), small perturbation method (SPM), integral equation method (IEM) and the semi-empirical polarimetic model. To apply the numerical technique of the MoM to microwave scattering from a rough surface, at first, many independent randomly rough surfaces with a rms height and a correlation length are generated with Gaussian random deviate. Then, an efficient Monte Carlo simulation technique is applied to estimate the scattering coefficients of the surfaces.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.558-560
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• 1995

Tunneling current from filed emission display tips is calculated by numerical analysis using a finite element method software. For simple tip structures it is shown that the image charge method could provide an efficient way to estimate the tunneling current.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.623-640
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• 2007

The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.