• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.381-391
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• 2012

In this paper, the formal linearization method is used to construct multisoliton solutions for three model of shallow water waves equations. The three models are completely integrable. The formal linearization method is an efficient method for obtaining exact multisoliton solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.1063-1067
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• 2005

A second-order accuracy upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with field observed data and results of a first-order accuracy upwind scheme, In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water The target events is 1993 Hokktaido Nansei Oki Tsunami. The predicted results represent reasonably the run-up heights of tsunamis in the East Sea. And, The results of simulation is used to design inundation map.

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

• Water Engineering Research
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• v.4 no.4
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• pp.175-185
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• 2003

A numerical model to analyze dam break flows has been developed based on approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using finite volume method and the numerical flux are reconstructed with weighted averaged flux (WAF) method. The developed model is verified. The first verification problem is about idealized dam break flow on wet and dry beds. The second problem is about experimental data of dam break flow. From the results of the verifications, very good agreements have been observed

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.4
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• pp.197-200
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• 1999

An extension of the modified leap-frog scheme is made to solve the nonlinear shallow-water equations. In the extended model. the physical dispersion of the Boussinesq equations is replaced by the numerical dispersion resulted from the leap-frog finite difference scheme. The model is used to simulate propagations of a solitary wave over a constant water depth and a linearly varying water depth. Obtained numerical results are compared with available analytical and other numerical solutions. A reasonable agreement is observed.

• Journal of computational fluids engineering
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• v.10 no.2
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• pp.7-14
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• 2005

In this study, the shallow water equations on the sphere is simulated by the proposed method which has high spatial resolution and is based on the CIP(Cubic Interpolated Pseudoparticle) method. The governing equations are approximated on the longitude-latitudinal coordinate system. To avoid the problems resulting from the convergence of the meridians toward high-latitude and singularities on the poles, the semi-Lagrangian and finite volume method are employed. in addition, the CIP method is employed to solve the advection equations and is extended to apply on the equations in the polar coordinate system. The mathematical formulation and numerical results are also described. To verify of the efficiency, accuracy and capability of proposed algorithm, the standard test cases proposed bv Williamson et. al are simulated and the results are compared with other results. As a result, it is found that the present scheme gives a good properties in preserving shapes of solution and settles the pole problems in solving the shallow water equations on the sphere.

• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.461-469
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• 2005

A second-order upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with the field data and results of a first-order upwind scheme. In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water. The target events are 1983 Central East Sea Tsunami and 1993 Hokkaido Nansei Oki Tsunami. The predicted results represent reasonably well the run-up heights of tsunamis in the East Sea. And, the results of simulation are used for the design of inundation map.

• International Union of Geodesy and Geophysics Korean Journal of Geophysical Research
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• v.26 no.1
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• pp.1-14
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• 1998

Various numerical methods for the two dimensional shallow water equations have been applied to the problems of flood routing, tidal circulation, storm surges, and atmospheric circulation. These methods are often based on the Alternating Direction Implicity(ADI) method. However, the ADI method results in inaccuracies for large time steps when dealing with a complex geometry or bathymetry. Since this method reduces the performance considerably, a fully implicit method developed by Wilders et al. (1998) is used to improve the accuracy for a large time step. Finite Difference Methods are defined on a rectangular grid. Two drawbacks of this type of grid are that grid refinement is not possibile locally and that the physical boundary is sometimes poorly represented by the numerical model boundary. Because of the second deficiency several purely numerical boundary effects can be involved. A boundary fitted curvilinear coordinate transformation is used to reduce these difficulties. It the curvilinear coordinate transformation is used to reduce these difficulties. If the coordinate transformation is orthogonal then the transformed shallow water equations are similar to the original equations. Therefore, an orthogonal coorinate transformation is used for defining coordinate system. A multigrid (MG) method is widely used to accelerate the convergence in the numerical methods. In this study, a technique using a MG method is proposed to reduce the computing time and to improve the accuracy for the orthogonal to reduce the computing time and to improve the accuracy for the orthogonal grid generation and the solutions of the shallow water equations.

• Water Engineering Research
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• v.2 no.3
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• pp.151-160
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• 2001

A two-dimensional flow model is newly developed. Two-dimensional shallow-water equations are discretized by the finite volume method. A nonorthogonal coordinate system is then employed. The developed model is applied to simulations of flows in a 180 degree curved bend flow. Numerical prediction are compared to available laboratory measurement. A good agreement is observed.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.53-65
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• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.