• Korean Journal of Hydrosciences
• /
• v.5
• /
• pp.85-97
• /
• 1994

A hybrid finite difference method for the longitudinal dispersion equation, which is based on combining the Holly-Preissmann scheme with fifth-degree Hermite interpolating polynomial and the generalized Crank-Nicholson scheme, is described and comparatively evaluated with other characteristics-based numerical methods. Longitudinal dispersion of an instantaneously-loaded pollutant source is simulated, and computational results are compared with the exact solution. The present method is free from wiggles regardless of the Courant number, and exactly reproduces the location of the peak concentration. Overall accuracy of the computation increases for smaller value of the weighting factor, $\theta$of the model. Larger values of $\theta$ overestimates the peak concentration. Smaller Courant number yields better accuracy, in general, but the sensitivity is very low, especially when the value of $\theta$ is small. From comparisons with the hybrid method using cubic interpolating polynomial and with splitoperator methods, the present method shows the best performance in reproducing the exact solution as the advection becomes more dominant.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.1B
• /
• pp.111-114
• /
• 2008

Explicit solutions of the wave dispersion equation are developed using the recursive relation in terms of the relative water depth. We use the solutions of Eckart (1951), Hunt (1979), and the deep-water and shallow-water solutions for initial values of the solution. All the recursive solutions converge to the exact one except that with the initial value of deep-water solution. The solution with the initial value by Hunt converged much faster than the others. The recursive solutions may be obtained quickly and simply by a hand calculator. For the transformation of linear water waves in whole water depth, the use of the recursive solutions will yield more accurate analytical solutions than use of previously developed explicit solutions.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2006.05a
• /
• pp.1935-1939
• /
• 2006

In this study, the new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects such as linear Boussinesq equations for the propagation of tsunamis. And, dispersion-correction factor is determined to mimic the frequency dispersion of the linear Boussinesq equations. The numerical model developed in this study is tested to the problem that initial free surface displacement is a Gaussian hump over a constant water depth, and the results from the numerical model are compared with analytical solutions. The results by present numerical model are accurate in comparison with the past models.

• Structural Engineering and Mechanics
• /
• v.55 no.2
• /
• pp.335-348
• /
• 2015

The influence of the interface imperfect bonding on the flexural wave dispersion in the bilayered hollow circular cylinder is studied with utilizing three-dimensional linear theory of elastodynamics. The shear-spring type model is used for describing the imperfect bonding on the interface between the layers and the degree of the imperfectness is estimated through the dimensionless shear-spring parameters which enter the mentioned model. The method for finding the analytical expressions for the sought values and dispersion equation are discussed and detailed. Numerical results on the lowest first and second modes are presented and analyzed. These results are obtained for various values of the shear-spring parameters. According to these results, in particular, it is established that as a results of the imperfection of the bonding between the layers the new branches of the dispersion related the first fundamental mode arise and the character of the dispersion curve related to the second mode becomes more complicated.

• 한국방재학회:학술대회논문집
• /
• 2007.02a
• /
• pp.395-398
• /
• 2007

In this study, new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects of the linear Boussinesq equations for the propagation of tsunamis. The new model is applied to near Gadeok island in Pusan about The Central East Sea Tsunami in 1983 and The Hokkaldo Nansei Oki Earthquake Tsunami in 1993 one simulated in the study.

• Journal of the Optical Society of Korea
• /
• v.12 no.4
• /
• pp.240-243
• /
• 2008

Using the well-known Fokker-Planck method, this paper presents a standard way to find the joint-characteristic function for the first- and second-order polarization-mode-dispersion vectors originally derived by Foschini and Shepp. Compared with the Foschini and Shepp's approach, the Fokker-Planck approach gives a more accurate and straightforward way to find the joint-characteristic function.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.26 no.4B
• /
• pp.335-344
• /
• 2006

In this study, sequential mixing model (SMM) was proposed based on the Taylor's theory which can be summarized as the fact that longitudinal advection and transverse diffusion occur independently and then the balance between the longitudinal shear and transverse mixing maintains. The numerical simulation of the model were performed for cases of different mixing time and transverse velocity distribution, and the results were compared with the solutions of 1-D longitudinal dispersion model (1-D LDM) and 2-D advection-dispersion model (2-D ADM). As a result it was confirmed that SMM embodies the Taylor's theory well. By the comparison between SMM and 2-D ADM, the relationship between the mixing time and the transverse diffusion coefficient was evaluated, and thus SMM can integrate 2-D ADM model as well as 1-D LDM model and be an explanatory model which can represents the shear flow dispersion in a visible way. In this study, the predicting equation of the longitudinal dispersion coefficient was developed by fitting the simulation results of SMM to the solution of 1-D LDM. The verification of the proposed equation was performed by the application to the 38 sets of field data. The proposed equation can predict the longitudinal dispersion coefficient within reliable accuracy, especially for the river with small width-to-depth ratio.

• 전기의세계
• /
• v.20 no.5
• /
• pp.15-18
• /
• 1971

Up to now, there have been numerous investigations about the effect of diffusion on the wave propagation in gaseous plasmas, but not so much in semiconductor magnetoplasmas. However, currently, it becomes the centor of interest to work with the latter problem, and this paper deals with the dispersion equation including diffusion effect in the latter case to see how diffusion affects the equation in which diffusion term is neglected in the first place, and the analysis is based on the assumption that the plasma can be treated as a hydrodynamical fluid, since, from a macroscopic view point, the plasma interacting with a magnetic field can be considered as a magneto-hydrodynamical fluid, an electrically conducting fluid subjected to electromagnetic force, and the system is linear. The results of the relation and computation show that in the non-streaming case the diffusion terms appear in the equation as perturbation terms and the amplitude of the wave vector changes parabolically with the variation of the angular frequency and the longitudinal modes are observed.

• Selected Papers of The Society of Naval Architects of Korea
• /
• v.1 no.1
• /
• pp.45-51
• /
• 1993

By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

• Journal of Soil and Groundwater Environment
• /
• v.18 no.3
• /
• pp.65-72
• /
• 2013

Adsorption of melamine was examined using columns packed with granular activated carbon (GAC). Raw GAC was sieved with 20, 40, 60 and 80 mesh to determine the influence of adsorbent particle size on reaction and diffusion. The mass ratio of the adsorption capacity of GAC for melamine ranged from 9.19 to 11.06%, and adsorption rates increased with decreasing particle size within this range. Rate constants between 3.295 ~ 4.799 $min^{-1}$ were obtained using a pseudofirst-order equation that was used to determine adsorption kinetics. A surface diffusion model was adapted to take into account the unsteady-state equation of a spherical adsorbent by converting the surface concentration from a constant to a variable governed by a dispersion equation. The calculated values were fit with the experimental results by using the diffusion coefficients as regression parameters. The modified equation exhibited a more precise agreement with respect to the sum of the absolute error (SAE).