• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.5 no.4
• /
• pp.307-317
• /
• 1993

The problem of sea wave transformation in the coastal zone taking into account effects of nonlinearity and disperison has been studied. Mathematical model for description of regular wave transformation is based on the method of nonlinear ray theory. The equations for rays and wave field have been produced. Nonlinear wave field is described by the modified Korteweg-de Vries equation. Some analytical solutions of this equation are obtained. Caustic transformation and dissipation effects are included in the mathematical model. Numerical algorithm of solution of the Korteweg-de Vries equation and its stability criterion are described. Results of nonlinear transformation of sea waves in the coastal zone are demonstrated.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.21 no.2
• /
• pp.117-126
• /
• 2009

In order to test the accuracy between the modified mild slope equation (MMSE) without evanescent modes and the plane-wave approximation (PA) of eigenfunction expansion method, various numerical results from both models are presented. In this study, analytical solutions of two models are employed, one based on the MMSE derived by Porter (2003) and the other on the scatterer method of PA by Seo (2008a). Judging from direct comparisons against existing results of rapidly varying topography, the PA model gives better predictions of the wave propagation than the MMSE model.

• Journal of Korean Society on Water Environment
• /
• v.23 no.1
• /
• pp.38-45
• /
• 2007

A one-dimensional kinematic wave model was used to calculate temporal and spatial changes of the highway runoff. Infiltration into pavement was considered using Darcy's law, as a function of flow depth and pavement hydraulic conductivity ($K_p$). The model equation was calculated using the method of characteristics (MOC), which provided stable solutions for the model equation. 22 storm events monitored in a highway runoff monitoring site in west Los Angeles in the U.S. were used for the model calculation and evaluation. Using three different values of $K_p$ ($5{\times}10^{-6}$, $10^{-5}$, and $2{\times}10^{-5}cm/sec$), total runoff volume and peak flow rate were calculated and then compared with the measured data for each storm event. According to the calculation results, $10^{-5}cm/sec$ was considered a site representative value of $K_p$. The study suggested a one-dimensional method to predict hydrodynamic behavior of highway runoff, which is required for the water quality prediction.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.11 no.2
• /
• pp.77-89
• /
• 1991

Based on Boussinesq equation, the parabolic approximation equation is used to analyse the propagation of shallow water waves with currents over slowly varying depth. Rip currents (jet-like) occur mainly in shallow waters where the Ursell parameter significatly exceeds the range of application of Stokes wave theory. We employ the nonlinear parabolic approximation equation which is valid for waves of large Ursell parameters and small scale currents. Two types of currents are considered; relatively strong and relatively weak currents. The wave propagating over rip currents on a sloping bottom experiences a shoaling due to the variations of depth and current velocity as well as refraction and diffraction due to the vorticity of currents. Numerical analyses for a nonlinear theory are valid before the breaking point.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.553-569
• /
• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Geophysics and Geophysical Exploration
• /
• v.26 no.3
• /
• pp.114-125
• /
• 2023

The physics-informed neural network (PINN) has been proposed to overcome the limitations of various numerical methods used to solve partial differential equations (PDEs) and the drawbacks of purely data-driven machine learning. The PINN directly applies PDEs to the construction of the loss function, introducing physical constraints to machine learning training. This technique can also be applied to wave equation modeling. However, to solve the wave equation using the PINN, second-order differentiations with respect to input data must be performed during neural network training, and the resulting wavefields contain complex dynamical phenomena, requiring careful strategies. This tutorial elucidates the fundamental concepts of the PINN and discusses considerations for wave equation modeling using the PINN approach. These considerations include spatial coordinate normalization, the selection of activation functions, and strategies for incorporating physics loss. Our experimental results demonstrated that normalizing the spatial coordinates of the training data leads to a more accurate reflection of initial conditions in neural network training for wave equation modeling. Furthermore, the characteristics of various functions were compared to select an appropriate activation function for wavefield prediction using neural networks. These comparisons focused on their differentiation with respect to input data and their convergence properties. Finally, the results of two scenarios for incorporating physics loss into the loss function during neural network training were compared. Through numerical experiments, a curriculum-based learning strategy, applying physics loss after the initial training steps, was more effective than utilizing physics loss from the early training steps. In addition, the effectiveness of the PINN technique was confirmed by comparing these results with those of training without any use of physics loss.

• Geomechanics and Engineering
• /
• v.31 no.6
• /
• pp.623-635
• /
• 2022

This paper presents the re-evaluation of existing piezocone penetration test (CPTu)-based shear wave velocity (V_s) equations through their application into well-documented data obtained at nine sites in six countries. The re-evaluation indicates that the existing equations are appropriate to use for any specific soil, but not for various types of clays. Existing equations were adjusted to suit all nine clays and show that the correlations between the measured and predicted V_s values tend to improve with an increasing number of parameters in the equations. An adjusted equation, which comprises a CPTu parameter and two soil properties (i.e., effective overburden stress and void ratio) with the best correlation, can be converted into a CPTu-based equation that has two CPTu parameters and depth by considering the effect of soil cementation. Then, the developed equation was verified by application to each of the nine soils and nine other worldwide clays, in which the predicted V_s values are comparable with the measured and the stochastically simulated values. Accordingly, the newly developed CPTu-based equation, which is a time-saving and economical method and can estimate V_s indirectly for any type of naturally deposited clay, is recommended for practical applications.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.315-327
• /
• 2007

Mathematical aspects of the electromagnetic surface-wave propagation are examined for the dielectric core consisting of multiple sub-layers, which are embedded in the gap between the two bounding cladding metals. For this purpose, the linear problem with a partial differential wave equation is formulated into a nonlinear eigenvalue problem. The resulting eigenvalue is found to exist only for a certain combination of the material densities and the number of the multiple sub-layers. The implications of several limiting cases are discussed in terms of electromagnetic characteristics.

• Journal of the Korean Society for Nondestructive Testing
• /
• v.23 no.6
• /
• pp.583-593
• /
• 2003

The effect of liquid confined in a pipe on elastic waves propagating in the pipe wall was studied theoretically and experimentally. The axisymmetric motion of the wave was modeled with the cylindrical membrane shell theory. The liquid pressure satisfying the axisymmetric wave equation was included in the governing equation as a radial load. The phase speed of the wave propagating in the axial direction was calculated, accounting for the apparent mass of the liquid. Experiments were performed in a pipe equipped with ring-shaped, piezoelectric transducers that were used for transmitting and receiving axisymmetric elastic waves in the pipe wall. The measured wave speeds were compared with the analytical ones. This work demonstrates the feasibility of using pipe waves for the determination of the density and, eventually, the flow rate of the liquid in a pipe.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2001.05a
• /
• pp.629-634
• /
• 2001

This study is to characterize the material property of early age high performance concrete emphasizing compressive strength using nondestructive testing methods. Three high performance concrete slabs of 600, 850 and 1100kg/$cm^{2}$ compressive strengths were prepared together with cylinders from same batches. Cylinder tests were peformed at the ages of 7, 14, 21 and 28 days after pouring. Using the impact echo method, the compression wave velocities were obtained based on different high performance concrete ages and compressive strengths. The equation to obtain the compressive strengths of high performance concrete has been developed using the obtained compression wave velocities. Using the SASW (spectral analysis of surface wave) method, the equation have also been developed to obtain the compressive strengths of high performance concrete based on the surface wave velocities.