• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1327-1335
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• 2002

The shock wave process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over the shock thickness which is comparable to the mean free path of the gas molecules involved. This shock wave fluid phenomenon is simulated by using the finite difference lattice Boltzmann method (FDLBM). In this paper, a new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of speeding up the calculation as well as stabilizing the numerical scheme. The numerical results of the proposed model show good agreement with the theoretical predictions.

• International Journal of Highway Engineering
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• v.17 no.5
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• pp.1-10
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• 2015

PURPOSES : A finite difference model considering snow melting process on porous asphalt pavement was derived on the basis of heat transfer and mass transfer theories. The derived model can be applied to predict the region where black-ice develops, as well as to predict temperature profile of pavement systems where a de-icing system is installed. In addition, the model can be used to determined the minimum energy required to melt the ice formed on the pavement. METHODS : The snow on the porous asphalt pavement, whose porosity must be considered in thermal analysis, is divided into several layers such as dry snow layer, saturated snow layer, water+pavement surface, pavement surface, and sublayer. The mass balance and heat balance equations are derived to describe conductive, convective, radiative, and latent transfer of heat and mass in each layer. The finite differential method is used to implement the derived equations, boundary conditions, and the testing method to determine the thermal properties are suggested for each layer. RESULTS: The finite differential equations that describe the icing and deicing on pavements are derived, and we have presented them in our work. The framework to develop a temperature-forecasting model is successfully created. CONCLUSIONS : We conclude by successfully creating framework for the finite difference model based on the heat and mass transfer theories. To complete implementation, laboratory tests required to be performed.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.468-474
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• 2001

The shock process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over a shock thickness which is comparable to the mean tree path of the gas molecules involved. The fluid phenomenon is simulated by using finite difference lattice Boltzmann method (FDLBM). In this research, the new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of shortening in calculation time and stabilizing in simulation operation. The numerical results agree also with the theoretical predictions.

• Steel and Composite Structures
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• v.27 no.3
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• pp.255-271
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• 2018

This paper deals with the transient dynamic analysis and elastic wave propagation in a functionally graded graphene platelets (FGGPLs)-reinforced composite thick hollow cylinder, which is subjected to shock loading. A micromechanical model based on the Halpin-Tsai model and rule of mixture is modified for nonlinear functionally graded distributions of graphene platelets (GPLs) in polymer matrix of composites. The governing equations are derived for an axisymmetric FGGPLs-reinforced composite cylinder with a finite length and then solved using a hybrid meshless method based on the generalized finite difference (GFD) and Newmark finite difference methods. A numerical time discretization is performed for the dynamic problem using the Newmark method. The dynamic behaviors of the displacements and stresses are obtained and discussed in detail using the modified micromechanical model and meshless GFD method. The effects of the reinforcement of the composite cylinder by GPLs on the elastic wave propagations in both displacement and stress fields are obtained for various parameters. It is concluded that the proposed micromechanical model and also the meshless GFD method have a high capability to simulate the composite structures under shock loadings, which are reinforced by FGGPLs. It is shown that the modified micromechanical model and solution technique based on the meshless GFD method are accurate. Also, the time histories of the field variables are shown for various parameters.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.4
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• pp.19-29
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• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2002.04a
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• pp.102-105
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• 2002

A new finite difference model is developed for solute transport in a fractured medium that can consider advection, adsorption, first-order decay, and scale-dependent dispersivity of individual fractures. In the model, the dispersivity of individual fractures is employed as a variable increasing with travel distance from a source. The model is verified using an analytical solution for a single fracture. A solution from the new model is independent of the outlet boundary condition of fractures, and has little numerical dispersion error.

• Journal of Korea Soil Environment Society
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• v.5 no.1
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• pp.3-12
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• 2000

The multi-region model, to describe preferential flow, is an equation representing solute transport in soils by dividing soil into numerous pore groups and using the hydraulic properties of the soil. As the model partial differential equation (PDE) is solved numerically with finite difference methods. a modified equivalent partial differential equation(MEPDE) of the partial differential equation of the multi-region model is derived to analyze the accuracy and consistency of the solution of the model PDE and the Von Neumann method is used to analyze the stability of the finite difference scheme. The evaluation obtained from the MEPDE indicated that the finite difference scheme was found to be consistent with the model PDE and had the second order accuracy The stability analysis is performed to analyze the model PDE with the amplification ratio and the phase lag using the Von Neumann method. The amplification ratio of the finite difference scheme gave non-dissipative results with various Peclet numbers and yielded the most high values as the Peclet number was one. The phase lag showed that the frequency component of the finite difference scheme lagged the true solution. From the result of the stability analysis for the model PDE, it is analyzed that the model domain should be discretized in the range of Pe < 1.0 and Cr < 2.0 to obtain the more accurate solution.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.503-508
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• 2016

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.6
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• pp.1921-1930
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• 1996

To design an optimum engine intake system, a flow model for the intake manifold was developed by the finite difference method. The flow in the intake manifold was one-dimensional, and the finite difference equations were derived from governing equations of flow, continuity, momentum and energy. The thermodynamic properties of the cylinder were found by the first law of thermodynamics, and the boundary conditions were formulated using steady flow model. By comparing the calculated results with experimental data, the appropriate boundary conditions and convergence limits for the flow model were established. From this model, the optimum manifold lengths at different engine operating conditions were investigated. The optimum manifold length became shorter when the engine speeds were increased. The effect of intake valve timings on inlet air mass was also studied by this model. Advancing intake valve opening decreased inlet air mass slightly, and the optimum intake valve closing was found. The difference in inlet air mass between cylinders was very small in this engine.

• Environmental Engineering Research
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• v.23 no.4
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• pp.442-448
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• 2018

This paper presents the numerical simulation of advection-diffusion mechanism of BOD concentration which was used as an indicator of waste only in one flow-direction of waste stabilization ponds (1-dimension (1-D)). This model was represented in partial differential equation order 2. The purpose of this paper was to determine the simulation of the model 1-D of wastewater transport phenomena based advection-diffusion mechanism and did validate the model. Numerical methods which was used for the solution of this model is finite difference method with Forward Time Central Space scheme. The simulation results which was obtained would be compared with field observation data as a validation model. Collection of field data was carried out in the Wastewater Treatment Plant Sewon, Bantul, D.I. Yogyakarta. The results of numerical simulations were indicate that the advection-diffusion mechanism takes place continuously over time. Then validation of the model was state that there was a difference between the calculation results with the field data, with a correlation value of 0.998.