• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.3
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• pp.129-138
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• 1993

In this study, the applicability of finite analytic method (FAM) is studied by selecting linearized-Burgers equation and Burgers equation which have convective and diffusive behaviors as the model equation of Navier-Stokes equations and by comparing numerical solution of finite difference method (FDM) and finite analytic method. The results are as follows. It is shown that the convergence of FAM for steady-state analytic solution of linearized-Burgers equation and Burgers equation is better than that of FDM under the same criteria. Also the accuracy of FAM for transient solution of Burgers equation is excellent. Especially, it is shown that oscillation phenomenon due to dispersion errors which occur according to the choice of grid size in FDM does not occur in FAM at all. So, it can be thought that FAM is numerically very stable scheme, which is free from dispersion errors.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.165-173
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• 1998

Analytical solutions to predict the movement rate of submerged mound are derived using the convection coefficient and the joint distribution function of wave heights and periods. Assuming that the sediment is moved onshore due to the velocity asymmetry of Stokes' second order nonlinear wave theory, the micro-scale bedload transport equation is applied to the sediment conservation. The nonlinear convection-diffusion equation can then be obtained which governs the migration of submerged mound. The movement rate decreases exponentially with increasing the water depth, but the movement rate tends to increase as the spectral width parameter, $ u$ increases. In comparison of the analytical solution with the measured data, it is found that the analytical solution overestimates the movement rate. However, the agreement between the analytical solution and the measured data is encouraging since this over-estimation may be due to the inaccuracy of input data and the limitation of sediment transport model. In particular, the movement rates with respect to the water depth predicted by the analytical solution are in very good agreement with the estimated result using the discritization technique with the hindcast wave data.

• Journal of Korea Water Resources Association
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• v.43 no.6
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• pp.543-557
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• 2010

The effects of the selection for sediment transport equations and advection-diffusion equations according to different sediment transport modes on the modeling results of bed changes were analyzed using the CCHE2D and compared with field data in this paper. The most suitable sediment transport equation and sediment transport mode for advection-diffusion equation were suggested for the upstream approached channel of the Nakdong River Estuary Barrage. The bed changes simulated by the Engelund and Hansen formula were very small in the modeling case for the low and high flow discharges compared with the case of the Ackers and White formula. Also, the numerical modeling with the actual hydraulic event in 2002 presents that the bed change result with the bed load transport type for advection-diffusion equation was close to the field measurement more than the suspended load type.

• Proceedings of the Korea Water Resources Association Conference
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• 1993.07a
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• pp.73-80
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• 1993

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.3
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• pp.859-871
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• 2014

In order to analyze the density current due to salt and temperature difference, this study develops new numerical model (LES-WASS-3D ver. 2.0) by introducing state equation for salt and temperature and 3D advection-diffusion equation to existing 3D numerical wave tank (LES-WASS-3D ver. 1.0). To verify the applicability, the newly-developed numerical model is analyzed comparing to the experimental result of existing numerical model. In the result, it well implement the behavior and vertical salt concentration of advected and diffused seawater as well as flow velocity and temperature of the discharged warm water. This confirms the validity and effectiveness of the developed numerical model.

• Journal of the Korean Society of Visualization
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• v.20 no.3
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• pp.74-85
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• 2022

We propose a Cubic-Interpolated Pseudo-Particle Lattice Boltzmann method (CIP-LBM) for the convection-diffusion equation (CDE) based on the Bhatnagar-Gross-Krook (BGK) scheme equation. The CIP-LBM relies on an accurate numerical lattice equilibrium particle distribution function on the advection term and the use of a splitting technique to solve the Lattice Boltzmann equation. Different schemes of lattice spaces such as D1Q3, D2Q5, and D2Q9 have been used for simulating a variety of problems described by the CDE. All simulations were carried out using the BGK model, although another LB scheme based on a collision term like two-relation time or multi-relaxation time can be easily applied. To show quantitative agreement, the results of the proposed model are compared with an analytical solution.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.2
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• pp.40-49
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• 1999

A Finite Volume Method for the two-dimensional incompressible, two-fluids Navies-Stokes equation and level-set scheme are used to analyse the interface of two fluids, free-surface flow. The numerical characteristics and the applicability of level-set scheme are brief1y investigated and appraised by solving oscillating small surface wave in a water tank and dam break problems. In the numerical results, a method for improving the convergence of the solution is presented.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.419-426
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• 2009

To realistically simulate fluid, the Navier-Stokes equations are generally used. Solving these Navier-Stokes equations on the Eulerian framework, the non-linear advection terms invoke heavy computation and thus Semi-Lagrangian methods are used as an approximated way of solving them. In the Semi-Lagrangian methods, the locations of advection sources are traced and the physical values at the traced locations are interpolated. In the case of Stam's method, there are relatively many chances of numerical losses, and thus there have been efforts to correct these numerical errors. In most cases, they have focused on the numerical interpolation processes, even simultaneously using particle-based methods. In this paper, we propose a new approach to reduce the numerical losses, through improving the tracing method during the advection calculations, without any modifications on the Eulerian framework itself. In our method, we trace the grids with the velocities which will let themselves to be moved to the current target position, differently from the previous approaches, where velocities of the current target positions are used. From the intuitive point of view, we adopted the simple physical observation: the physical quantities at a specific position will be moved to the new location due to the current velocity. Our method shows reasonable reduction on the numerical losses during the smoke simulations, finally to achieve real-time processing even with enhanced realities.

• Journal of Soil and Groundwater Environment
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• v.12 no.5
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• pp.33-36
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• 2007

In recent years the convective-dispersive equation has been often discredited in predicting subsurface solute transport under field conditions due to presence of preferential flow paths. Kim et al. (2005) proposed a simple equation that can predict the breakthrough of solutes without excessive data requirements. In their Generalized Preferential Flow Model (GPFM), the soil is conceptually divided in a saturated "distribution layer" near the surface and a "conveyance zone" with preferential flow paths below. In this study, we test the model with previously published data, and compare it with a classical convective-dispersive model (CDM). With three parameters required-apparent water content of the distribution zone, and solute velocity and dispersion in the conveyance zone-GPFM was able to describe the breakthrough of solutes both through silty and sandy loam soils. Although both GPFM and CDM fitted the data well in visual, variables for GPFM were more realistic. The most sensitive parameter was the apparent water content, indicating that it is the determining factor to apply GPFM to various soil types, while Kim et al. (2005) reported that changing the velocity of GPFM reproduced solute transport when same soils were used. Overall, it seems that the GPFM has a great potential to predict solute leaching under field conditions with a wide range of generality.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.2
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• pp.137-145
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• 1996

Effects of nonlinear terms on the generation of M$_2$ tide residual elevation and M$_4$ tide in the Yellow Sea and the East China Sea are investigated using a depth-integrated two-dimensional nonlinear M$_2$tidal model. The model domain (117$^{\circ}$E-130$^{\circ}$E, 24$^{\circ}$N-41$^{\circ}$N) covers the whole region of the Yellow Sea and the East China Sea with grid resolution of 1/6$^{\circ}$ in longitude and 1/8$^{\circ}$in latitude. A radiational boundary condition is used along the open boundaries. Calculations show that advection terms yield negative residual elevation, while shallow-water terms in continuity equation yield positive residual elevation. The contribution of both advection terms and shallow-water terms to tile generation of the M$_4$ constituent is more than 90 percents, but that of quadratic bottom friction terms to the M$_4$ constituent is comparatively small.