• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.1
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• pp.41-52
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• 1989

Numerical characteristics for the shallow water equation are analyzed with ADI, Hansen, Heaps, Richtmyer and MacCormack schemes. Stability, CPU time and accuracy are investigated for the linear model which has analytic solutions and circulation is simulated for the nonlinear model. The results show that ADI method has some defects in CPU time and accuracy for the computation of velocity. But ADI method simulates circulation well and has the largest stability region. Richtmyer scheme is the best among the other explicit schemes. Effective viscosity term is found to be essential for numerical experiments of the shallow water equation.

• East Asian mathematical journal
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• v.33 no.1
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• pp.53-65
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• 2017

Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.51-56
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• 2000

The Finite Element Solutions Is reported on solid-liquid phase change in porous media with natural convection including freezing. The model is based on volume averaged transport equations, while phase change is assumed to occur over a small temperature range. The FEM (Finite Element Method) algorithm used in this study is 3-step time-splitting method which requires much less execution time and computer storage the velocity-pressure integrated method and the penalty method. And the explicit Lax-Wendroff scheme is applied to nonlinear convective term in the energy equation. For natural convection including melting and solidification the numerical results show reasonable agreement with FDM (Finite Difference Method) results.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.58-69
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• 1995

The present paper is devoted to constructing a numerical algorithm for solving un steady problems on generation, propagation and interaction of nonlinear waves at a surface of ideal fluid, within the framework of the potential-flow model. The numerical scheme is implicit. with non-linearity iteration at every step of time. the finite-difference method with boundary-fitted coordinates are presented in favor for validity and high efficiency of the numerical model developed. Among these arguments, there are the results of calculations of two test problems-on stretching of a liquid ellipse and on wave generation by lifting a portion of a bottom.

• Journal of Industrial Technology
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• v.20 no.A
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• pp.139-148
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• 2000

A numerical model is represented to calculate the wave fields such as the reflected waves, the transmitted waves, and depth averaged velocities over submerged breakwaters for the normally incident wave trains of nonlinear monochromatic wave. The numerical model is correctly formulated by using both the finite amplitude shallow water equations with the effects of bottom friction and the explicit dissipative Lax-Wendroff finite difference scheme, also satisfactorily verified by comparison with the other results. The behaviors of reflected and transmitted waves with respect to geometric parameters of submerged breakwater such as the slope, crest depth, and crest width are numerically analyzed in this study. In particular, the reflection and transmission coefficients are quantitatively calculated as the function of geometric parameter of submerged breakwater. It is found that the crest depth among parameters related to practical design may be the most important parameter in designing the submerged breakwater. Therefore, the effective and economic performances of submerged breakwater should be depended on the determination of optimal crest depth.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1975-1981
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• 1991

A new numerical solution of the elastohydrodynamic lubrication(EHL) problem of an axially profiled cylindrical roller is presented. A finite difference method and the Newton-Raphson method are used to solve the nonlinear system equations. A non-uniform grid system is adopted to reduce the number of grid points and to obtain accurate solution. For two different types of profiles which have similar elastostatic pressure distribution, the EHL results show large differences. Especially the difference in film shape is larger than in pressure distribution. Therefore, the magnitude of the minimum film thickness should be a major criteria to design the axial profile of the roller. Variations of the minimum film thickness with dimensionless parameters show considerably different behavior from those of infinite solution and show a good agreement with the experimental data in literatures. Present numerical scheme can be used generally in the analysis of three-dimensional EHL problem.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1303-1309
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• 2018

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.6
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• pp.348-357
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• 2021

In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

• Journal of Korean Society on Water Environment
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• v.23 no.5
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• pp.683-688
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• 2007

Water flow into unsaturated soils is most often modeled by Richards equation consisting of the mass conservation law and Darcy's law. Three standard forms of Richards equation are presented as the head (${\Psi}$)-based form, the moisture content (${\theta}$) based form, and the mixed form. Numerical solutions of these partial differential equations with highly nonlinear terms can cause poor results along with significant mass balance errors. The numerical solution based on the mixed form of Richards equation is known that the mass is perfectly conserved without any additional computational efforts. The aim of this study is to develop fully implicit numerical scheme of Richards equation for one-dimensional vertical unsaturated flow in homogeneous soils using the finite difference approximation, and then to perform sensitivity analysis of infiltration to the variations in the unsaturated soil properties and to different soil types.

• Geotechnical Engineering
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• v.1 no.1
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• pp.5-12
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• 1985

Ocassionally it is used for simple extensions of Terzahgi's theory to account for time-depend- tint loading but there is little evidence of application in more complicated consolidation theories that take into account such effects as nonlinear stress.strain, layered systems or large strains. The purpose of this paper provides an efficient computer algorthm based on numerical analysis using finite difference method which account for multi-layered soils to determine the degree of consolidation and excess pore pressures relative to time and positions more realistically. The explicitly scheme of solving the consolidation equations has been investigated from the point of view of the stability conditions and the convergence with variance of the operator as well as to obtain an optimal divided depth ratios of total depth. A comparison of the settlement predictions with both the classical analysis and the algorithm based on numerical analysis indicates that the new algorithm scheme is found to be superior to the classical theory in the layered soils.