• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회(2)
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• pp.842-845
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• 2005

A method for the numerical simulation of two-dimensional free-surface flow resulting from the propagation of regular gravity waves over topography with arbitrary bottom shape is presented. The method is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. The formulation includes a boundary-fitted transformation, and is suitable for extension to incorporate large-eddy simulation (LES) and large-wave simulation (LWS) terms for turbulence and breaking wave modeling, respectively. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:20, two different inflow wave lengths and two different inflow wave heights. An absorption outflow zone is utilized and the results indicate minimum wave reflection from the outflow boundary. Over the bottom slope, lengths of waves in the linear regime are modified according to linear theory dispersion, while wave heights remain more or less unchanged. For waves in the nonlinear regime, wave lengths are becoming shorter, while the free surface elevation deviates from its initial sinusoidal shape.

• International Journal of Aerospace System Engineering
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• 제2권2호
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• pp.58-61
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• 2015

Combustion instability in solid rocket motors is a long-term open problem since the first rockets were used. Based on the numerous previous studies, it is known that the limit cycle amplitude is one of the key characteristics of the nonlinear combustion instability in solid rocket motors. Flandro's extended energy balance corollary, aims to predict the limit cycle amplitude of complex, nonlinear pressure oscillations for rockets or air-breathing engines, and leads to a precise assessment of nonlinear combustion instability in solid rocket motors. However, based on the comparison with experimental data, it is revealed that the Flandro's method cannot accurately describe such a complex oscillatory pressure. Thus in this work we make modifications of the nonlinear term in the nonlinear wave equations which represents the interaction of different modes. Through this modified method, a numerical simulation of the cylindrical solid rocket has been carried out, and the simulated result consists well with the experimental data. It means that the added coefficient makes the nonlinear wave growth equations describe the experimental data better.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.119-130
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• 2002

An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means.

• International Journal of Naval Architecture and Ocean Engineering
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• 제3권3호
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• pp.159-173
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• 2011

The two different numerical approaches for solving the nonlinear ship wave problem are discussed in the present paper. One is based on a panel method, which neglects the viscous effects. The other is based on a finite volume method, which take into account the viscous effects by solving RANS equations. Focus is laid upon on the advantages and disadvantages of two methods. The developed methods are applied to calculating the flow around Series 60 hull to validate the performance of the present nonlinear methods. Although the two methods employ quite different numerical approaches, the calculated wave patterns from both methods show good agreements with the experiments. However the potential method simu-lates the global wave pattern accurately, while the viscous method shows better performance for the local wave prediction near a ship.

• 한국해양공학회지
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• 제10권3호
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.261-273
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• 2015

We consider the hyperelastic rod equation describing nonlinear dispersive waves in compressible hyperelastic rods. We investigate the existence of certain traveling wave solutions to this equation. We also determine whether two other equations(the b-family equation and the modified Camassa-Holm equation) have our solution type.

• 한국전산유체공학회지
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• 제2권1호
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• pp.13-20
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• 1997

A fundamental study for the numerical scheme to simulate unsteady nonlinear waves by solving Euler equations is presented. First a conservation form and a non-conservation form of the Euler equations with a free surface fitted coordinate system are compared. Next, a time splitting fractional step method and an alternating direction implicit(ADI) method for the time integration are compared. For the comparative study, flow calculations around a bottom bump in a channel and a NACA 0012 hydrofoil in a flume are performed. The results show that the ADI method with a third order upwind differencing scheme is very efficient in reducing the computing time with keeping the accuracy, And, there is no distinct difference between two expression forms except that the non-conservative form shows faster wave propagating velocity than the conservation form. Some results are compared with experiments and show good agreement.

• 한국해안·해양공학회논문집
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• 제23권5호
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• pp.335-344
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• 2011

곡면의 경계를 가지는 수로에서 비선형 파랑의 상호작용을 모의하기 위한 비정수압 자유수면 모형이 개발되었다. 제안된 모형은 비선형의 3차원 Navier-Stokes 방정식을 곡선좌표 영역에서 계산단계 분리법의 일종인 압력수정법에 의하여 수치적으로 해석된다. 특히, 연직방향으로 변형된 형태의 엇갈린 격자를 이용하여 상대적으로 간단하게 압력방정식과 자유수면 경계조건을 구성하였다. 개발된 모형의 수치해석 정확도는 2차원의 수치 파수조에서 파랑의 비선형 정도에 대하여 5차의 스토스우크스 해석해와 비교하였다. 본 모형의 실제적 적용은 원형의 수로에서 회절과 반사에 의해 변형되는 비선형 파의 변형에 초점을 맞추어 수행하였다. 두개의 파를 중첩한 고비선형의 파에 대한 경우를 제외하고 수치해석 결과는 비선형적인 영향을 고려하지 않은 해석해의 선형적인 중첩과 일치하였다. 두개의 파를 중첩한 고비선형의 파에 대한 모의를 통하여 본 모형은 원형의 수로에서 비선형 군파의 변형에관한 수치적인 모의 가능성을 제시하였다.

• 한국수자원학회논문집
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• 제38권6호
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• pp.429-438
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• 2005

본 연구에서는 Boussinesq 방정식을 이용하여, 불규칙 파랑의 직접적인 해석이 가능한 한 쌍의 상미분방정식을 유도하였다. 입사파랑은 TMA(TEXEL storm, MARSEN, ARSLOE) 천해 스펙트럼을 이용하여 재현하였으며, 지배방정식은 4차 Runge-Kutta 법을 이용하여 적분하였다. 새로 유도된 파랑 방정식을 이용하여, 일정 수심을 진행하는 파랑의 비선형 에너지 교환효과를 계산하였다. 또한, 일정 경사면의 정현파형 지형을 통과하는 불규칙파랑의 특성에 관해 수치적으로 검토하였다. 비선형성이 불규칙파랑의 통과와 반사에 큰 영향을 주었다.