• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.293-303
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• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1129-1141
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• 2011

In this paper, a class of large time-stepping method based on the finite element discretization for the Cahn-Hilliard equation with the Neumann boundary conditions is developed. The equation is discretized by finite element method in space and semi-implicit schemes in time. For the first order fully discrete scheme, convergence property is investigated by using finite element analysis. Numerical experiment is presented, which demonstrates the effectiveness of the large time-stepping approaches.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.5-10
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• 2003

In order to reduce the excessive numerical dissipation, the new spatial discretization scheme is introduced. The present method in this paper has the formula that has an additional procedure of defining transferred properties at a cell-interface, based on AUSMPW+. The newly defined transferred property could eliminate numerical dissipation effectively in non-flow aligned grid system. In addition, the present method guarantees the monotonic characteristic in capturing a discontinuity. Through a stationary or moving contact discontinuity and a stationary or moving shock discontinuity, a vortex discontinuity and shock wave/ boundary layer interaction, it is verified that the accuracy of the present method is improved.

• Journal of electromagnetic engineering and science
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• v.8 no.3
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• pp.100-109
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• 2008

The finite volume time domain(FVTD) technique faces serious limitations in simulating electromagnetic scattering at high frequencies due to requirements related to discretization. A modified FVTD method is proposed for electrically large, perfectly conducting scatterers by partially incorporating a time-domain physical optics(PO) approximation for the surface current. Dominant specular returns in the modified FVTD method are modeled using a PO approximation of the surface current allowing for a much coarser discretization at high electrical sizes compared to the original FVTD scheme. This coarse discretization can be based on the minimum surface resolution required for a satisfactory numerical evaluation of the PO integral for the scattered far-field. Non-uniform discretization and spatial accuracy can also be used in the context of the modified FVTD method. The modified FVTD method is aimed at simulating electromagnetic scattering from geometries containing long smooth illuminated sections with respect to the incident wave. The computational efficiency of the modified FVTD method for higher electrical sizes are shown by solving two-dimensional test cases involving electromagnetic scattering from a circular cylinder and a symmetric airfoil.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.455-466
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• 1999

In this note we present a numerical scheme for finding an approxximate solution of an equation which can be viewed as a model for spatial diffusion of age-depednent biological populations. Discretization of the model yields a linear system with a block tridi-agonal matrix. Our main concern will be discussion of stability for this scheme by examining the eigenvalues of the block tridiagonal matrix. Numerical results are presented.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.31-36
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• 2003

A field reconstruction scheme for a cell centered finite volume method on unstructured meshes is developed. Regardless of mesh quality, this method is exact within a machine accuracy if the solution is linear, which means it has full second order accuracy. It does not have any limitation on cell shape except convexity of the cells and recovers standard discretization stencils at structured orthogonal grids. Accuracy comparisons with other popular reconstruction schemes are performed on a simple example.

• Journal of Korean Society of Water and Wastewater
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• v.25 no.5
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• pp.635-642
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• 2011

Hydraulic efficiency was a vital component in evaluating the disinfection capability of clearwell. Current practice evaluates these system based on the tracer test only. In this paper, CFD(Computational Fluid Dynamics) was applied on the clearwell for alternating or supplementing the tracer test. The baffle factor derived from the CFD modeling closely matched the values obtained from full scale tracer testing. And, for suggesting proper numerical model in clearwell; the turbulence model, discretization scheme, convergence criteria were investigated through separate simulation runs. The model validation was conducted by comparing the simulated data with experimental data. In the turbulence model, the realizable ${\kappa}-{\varepsilon}$ model and the standard ${\kappa}-{\varepsilon}$ model were found to be more appropriate than RNG ${\kappa}-{\varepsilon}$ model. The residuals of convergence criteria should be used as not $10^{-3}$ but $10^{-4}$ or $10^{-5}$. In discretization scheme, the difference of simulated values in 1st, 2nd, 3rd upwind scheme was found to be insignificant. Moreover, the result of this study suggest that CFD modeling can be a reliable alternative to tracer testing for evaluating the hydraulic efficiency.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.5
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• pp.694-698
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• 2000

In the cylindrical coordinate, the origin r = 0 plays a role of the singularity and thus much care is needed to treat near-origin region. This work presents a new numerical scheme which is derived from the exact solution under the one-dimensional assumption in the radial direction. It is shown that the near-origin region can be properly treated by the radial-exponential scheme, whereas the numerical results from the conventional exponential scheme deviate considerably from the exact solution. Over the region of small ($ {\delta}r_e/r_e$ the present radial-exponential scheme turns out to be almost the same as the exponential scheme.

• 한국전산유체공학회:학술대회논문집
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• 2000.10a
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• pp.135-140
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• 2000

Numerical calculations are carried out in order to evaluate the performance of low-Re Reynolds stress model based on SSG model for a swirling turbulent flow in a pipe. The results are compared with those of $\kappa-\epsilon$ model and GL model, and the experimental data. The finite volume method is used for the discretization, and the power-law scheme is employed as a numerical scheme. The SIMPLE algorithm is used for velocity-Pressure correction in the governing equations.