• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.11
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• pp.1521-1530
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• 2002

This article proposes a pressure based method for predicting flows at all speeds. The compressible SIMPLE algorithm is extended to unstructured grid framework. Convection terms are discretized using second-order scheme with deferred correction approach. Diffusion term discretization is based on structured grid analogy that can be easily adopted to hybrid unstructured grid solver. This method also uses node centered scheme with edge based data structure for memory and computing time efficiency of arbitrary grid types. Both incompressible and compressible benchmark problems are solved using the above methodology. The demonstration of this method is extended to slip flow problem that has low Reynolds number but compressibility effect. It is shown that the proposed method can improve efficiency in memory usage and computing time without losing any accuracy.

• Journal of Industrial Technology
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• v.19
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• pp.391-402
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• 1999

The numerical model predicting the behaviours of submerged mound constructed by dredged material is developed in this paper. The model is based on the Bailard's sediment transport formula, Stokes' second-order wave theory and the sediment balance equation. Nonlinear partial differential equation which is the same form as convection-dispersion equation which represents change of bed section can be obtained by substituting sediment transport equation for equation of sediment conservation. By this process, the analytical solution by which the characteristic of the behaviours of submerged mound can be estimated is derived by probably combining the convention coefficient and the dispersion coefficient governing the behaviours of submerged mound and the probability density function representing the wave characteristics. The validity of the analytical solution is verified by comparing the analytical solution which is assumed to estimate the movement rate submerged mound by bed-load with the field data of the past and its characteristic is analyzed quantitatively by obtaining the mean of the dispersion coefficient representing the extent of the decrease rate of the submerged mound height.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2000.02a
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• pp.35-38
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• 2000

A preliminary design of gas-gp thermal switch is presented to reduce the cooldown time of superconducting system conduction-cooled by a two-stage refrigerator without liquid cryogens. The switch connects thermally the first and the second stages (ON) to take advantage of the larger refrigeration capacity at the first stage during the beginning period. After the cryogenic temperature is reached, the switch should isolate thermally the two stages (OFF) in order to reduce the heat leak to the cold end. In this paper, a new concept for the performance index is introduced to evaluate the reduction of the cooldown time and the increase of the cooling load at the same time. In addition, the design of a gas-gap switch is discussed as a closed container of several staggered concentric tubes filled with gas, which is frozen at low temperatures for the shut-off of heat without any mechanical actuation. Some of the detailed features in the design is quantitative investigated by the gas convection model in the continuum or the rarefied gas region.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Geomechanics and Engineering
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• v.8 no.2
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• pp.133-152
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• 2015

Mathematical model has been developed for determination of temperature field in multilayer pavement and subgrade, which considers transfer of heat by conduction and convection, receiving of heat from total solar radiation and atmosphere emission, output of heat due to the emission from the surface of pavement. The developed model has been realized by the finite element method for two dimensional problem using two dimensional second order finite element. Calculations for temperature field have been made with the programme realized on the standard mathematical package MATLAB. Accuracy of the developed model has been evaluated by comparison of temperatures, obtained theoretically and experimentally. The results of comparison showed high accuracy of the model. Long-term calculation (within three months) has been made in pavement points in accordance with the data of meteorological station for air temperature. Some regularities have been determined for variation of temperature field.

• Journal of the Korean Society of Hazard Mitigation
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• v.8 no.2
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• pp.159-164
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• 2008

This study simulated the flood inundations of the Nakdong River catchment running through Yangsan, a small city located in the south eastern area of Korea by using the depth averaged two-dimensional hydrodynamic numerical model. The numerical model employs the staggered grid system including moving boundary and a finite different method to solve the Saint-Venant equations. A second order upwind scheme is used to discretize the nonlinear convection terms of the momentum equations, whereas linear terms are discretized by a second order Leap-frog scheme(Cho and Yoon, 1998). The numerical model was applied to a real topography to simulate the flood inundation of the Yangsan basin in Yangsan. The numerical result for urban district was visualization for three dimension. These results can be essentially utilized to construct the three dimensional inundation map after building the GIS-based database in local public organizations in order to protect the life and property safely.

• Journal of Energy Engineering
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• v.12 no.1
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• pp.29-34
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• 2003

Thermo-acoustic waves can be generated in a compressible fluid by rapid heating and cooling near the boundary walls. These phenomena are very important mechanism of heat transfer in the space environment in which natural convection does not exist. In this study, the generation and transmission characteristics of thermo-acoustic waves in an air filled enclosure with rapid wall heating are studied numerically. The governing equations were discretized using control volume method, and were solved using PISO algorithm and second-order upwind scheme. For the stable solution time step were considered as t=1$\times$$10^{-9}$ order, and grids are 50$\times$800. The induced thermo-acoustic wave propagates through the fluid until it decays due to viscous and heat dissipation. The wave showed sharp front shape and decreased with long tail.

• Wind and Structures
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• v.15 no.3
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• pp.189-208
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• 2012

Lock-in and drag amplification phenomena are studied for a flexible cantilever using a simplified fluid-structure interaction approach. Instead of solving the 3D domain, a simplified setup is devised, in which 2D flow problems are solved on a number of planes parallel to the wind direction and transversal to the structure. On such planes, the incompressible Navier-Stokes equations are solved to estimate the fluid action at different positions of the line-like structure. The fluid flow on each plane is coupled with the structural deformation at the corresponding position, affecting the dynamic behaviour of the system. An Arbitrary Lagrangian-Eulerian (ALE) approach is used to take in account the deformation of the domain, and a fractional-step scheme is used to solve the fluid field. The stabilization of incompressibility and convection is achieved through orthogonal quasi-static subscales, an approach that is believed to provide a first step towards turbulence modelling. In order to model the structural problem, a special one-dimensional element for thin walled cross-section beam is implemented. The standard second-order Bossak method is used for the time integration of the structural problem.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.14 no.11
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• pp.914-922
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• 2002

Thermo-acoustic waves can be thermally generated in a compressible flow field by rapid heating and cooling, and chemical reaction near the boundary walls. This mechanism is very important in the space environment in which natural convection does not exist. Also this may be a significant factor for heat transfer when the fluids are close to the thermodynamic critical point. In this study, the generation and transmission characteristics of thermo-acoustic waves in an air-filled confined domain with two-step pulsed heating are studied numerically. The governing equations are discretized using control volume method, and are solved using PISO algorithm and second-order upwind scheme. For the purpose of stable solution, time step was set to the order of $1\times10_-9s,\;and\;grids\;are\;50\times2000$. Results show that temperature and pressure distributions of fluid near the boundary wall subjected to a rapid heating are increased abruptly, and the induced thermo-acoustic wave propagates through the fluid until it decays due to viscous and heat dissipation. Pressure waves have sharp front shape and decay with a long tail in the case of step heating, but these waves have sharp pin shape in the case of pulsed heating.