• Title/Summary/Keyword: 비선형 파동방정식

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Nonlinearity of semiconductor optical amplifier and gain-clamping effects of Iaser-injected semiconductor optical amplifier in wavelength division mulitiplexing (파장 다중 광통신에서의 반도체 광증폭기의 비선형성과 연속파동 레이저가 입사된 반도체 광증폭기의 이득고정 효과)

  • 김동철;유건호;김형문;주흥로;한선규;주관종
    • Korean Journal of Optics and Photonics
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    • v.11 no.1
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    • pp.37-42
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    • 2000
  • We have numerically solved rate-equations of semiconductor optical amplifier (SOA) to understand the characteristics of SOA. The rate-equations we have used can describe injection carrier density, amplified spontaneous emission and signal photon density in spatial and time domain by dividing the cavity into multi-section. We have investigated injection carrier density, amplified spontaneous emission and signal photon density as a function of position and time in the case of single channel input in the form of square pulse. Also we have analyzed the non-linear phenomena of SOA in the case of injecting multi-channel wavelengths as in WDM. Intermodulation distortion (IMD) caused by beat among channels has significant effects on the signal distortion as the channel spacing becomes narrower, and channel crosstalk becomes larger as the power of signals increases. In the case of the injection of another CW laser whose wavelength is far enough from the signal wavelengths, the crosstalk and the output signal distortion can be significantly reduced. duced.

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Coastally Trapped Waves over a Double Shelf Topography(II) : Free Waves with Linear Topographies (양향성 대륙붕의 대륙붕파 (II): 선형함수적 해저지형에서의 자유파)

  • PANG Ig-Chan
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.25 no.6
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    • pp.443-456
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    • 1992
  • For a linear double shelf bottom topography as in the Yellow Sea, the dispersion relation of coastally trapped waves is derived for the general case Including high-frequency and short waves and for the case of low-frequency and long waves. With linear bottom topography, the governing equation is Bessel's equation for the latter case but Hummer's equation for the former case. Hypergeometric Functions, which are the solutions of Hummer's equation, are derived and converted to various special functions for the limiting cases. On a double shelf topography, the divergence effects of horizontal flow are important for the wave dynamics, irrespective of cross-shelf dimensions, while on a single shelf they are usually neglected when the cross-shelf dimension is much smaller than the Rossby deformation radius. The divergence effect allows the existence of Kelvin wave and reduces the phase speeds of continental shelf waves. Finally, the frictionless eigenfunctions are proved to be orthogonal.

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On Overtopping Characteristics of Tsunami due to Waveforms (파형에 따른 지진해일의 월파특성에 관한 고찰)

  • Lee, Woo-Dong;Kim, Jung-Ouk;Park, Jong-Ryul;Hur, Dong-Soo
    • Proceedings of the Korea Water Resources Association Conference
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    • 2017.05a
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    • pp.142-146
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    • 2017
  • 지진해일의 수리특성을 분석하기 위하여 유사한 파형특성을 가진 고립파를 많이 이용하고 있다. 그러나 고립파의 근사파형은 실제 지진해일에 비해 상당히 좁은 파형분포를 가지고 있다. 이에 수치모의에서는 기존의 고립파 근사식을 개량하여 고립파형의 지진해일을 수치적으로 생성하고 있다. 본 연구에서는 지진해일의 파형분포에 따른 월파특성을 수치적으로 조사하기 위하여 개량된 고립파 근사식을 2차원 N-S solver에서 적용하였다. 이것에 기초하여 수치파동수조에 직립호안과 그 배후에는 월파수조를 설치하고, 지진해일 월파량을 측정하였다. 수치해석결과로부터 직립호안 주변의 공간파형과 마루 위의 유속분포로부터 파형분포에 따른 월파현상을 분석할 수 있었다. 또한 기존 고립파 근사이론 대비 개량된 고립파의 체적비에 따른 월파량 변화를 정량적으로 조사하였다. 그 결과 지진해일의 체적비가 증가할수록 월파량이 거의 선형적으로 증가하는 경향을 나타내었다.

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Development and verification of a combined method of BEM and VOF (BEM과 VOF법을 결합한 수치모델의 개발과 그 타당성 검토)

  • Kim Sang-Ho;Yamashiro Masaru;Yoshida Akinori;Hashimoto Noriaki;Lee Joong-Woo
    • Journal of Navigation and Port Research
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    • v.29 no.10 s.106
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    • pp.853-858
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    • 2005
  • Recently, various novel numerical models based on Navier-Stokes equation have been developed for calculating wave motions in the sea with coastal or ocean structures. Among those models, Volume Of Fluid (VOF) method might be the most popular one, and it has been used for numerical simulations of wave motions including complicated phenomena of wave breakings. VOF method, however, needs enormous computation time and large computational storage memories in general, thus it is practically difficult to use this method for calculations in the case of random waves because long and stable computation (e.g for more than 100 significant wave periods) is required to obtain statistically meaningful results. On the other hand if the wave motion is potential motion, Boundary Element Method (BEM), which is a much faster and more accurate method than VOF method, can be effectively used. The aim of this study is to develop a new efficient model applicable to calculations of wave motion and/or wave-structure interactions under random waves. To achieve this, a strictly combined BEM-VOF model has been developed by making the best use of both methods' merits; VOF method is used in a restricted fluid domain around a structure where complicated phenomena of wave breakings may exist, and BEM is used in the other domains far from the disturbance where the wave motion may be assumed to be potential. The verification of the model was performed with numerical results for Stokes' 5th order wave propagation and a random wave propagation.

Development and verification of a combined method of BEM and VOF (BEM과 VOF법을 결합한 수치모델의 개발과 그 타당성 검토)

  • Kim Sang-Ho;Yannshiro Masaru;Yoshida Akinori;Hashimoto Noriaki;Lee Jong-Woo
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2005.10a
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    • pp.153-159
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    • 2005
  • Recently, various novel numerical models based on Navier-Stokes equation rave been developed for calculating wave motions in the sea with coastal or ocean structures. Among those models, Volume Of Fluid (VOF) method might be the most popular one, and it has been used for numerical simulations of wave motions including complicated phenomena of wave breakings. VOF method, however, needs enormous computation time and large computational storage memories in general, thus it is practically difficult to use VOF method for calculations in the case of random waves because long and stable computation ( e.g. for more than 100 significant wave periods) is required to obtain statistically meaningful results. On the other hand of the wave motion is potential motion, Boundary Element Method (BEM), which is a much faster and more accurate method than VOF method, am be effectively used. The aim of this study is to develop a new efficient model applicable to calculations of wave motion and/or wave-structure interactions under random waves. To achieve this, a strictly combined BEM-VOF model has been developed by making the best use of both methods' merits; VOF method is used in a restricted fluid domain around a structure where complicated phenomena of wave breakings may exist, and BEM is used in the other domains far from the disturbance where the wave motion may be assumed to be potential. The verification of the model was performed with numerical results for Stokes'5th order wave propagation and a random wave propagation.

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Wave Forces Acting on Large Vertical Circular Cylinder and Consequent Wave Transformations by Full-Nonlinear Analysis Method after Wave Breaking (강비선형해석법에 의한 대형연직원주구조물에 작용하는 쇄파후의 파력 및 파랑변형)

  • Lee, Kwang-Ho;Shin, Dong-Hoon;Kim, Do-Sam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.20 no.4
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    • pp.401-412
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    • 2008
  • Simulations of three-dimensional numerical wave tank are performed to investigate wave force acting on a large cylindrical structure and consequent wave deformation, which are induced by bore after breaking waves. The numerical model is based on the three-dimensional Navier-Stokes equations with a finite-difference method combined with a volume of fluid(VOF) method, which is capable of tracking the complex free surface, including wave breaking. In order to promote wave breaking of the incident wave, the approach slope was built seaward of the structure with a constant slope and a large cylindrical structure was installed on a flat bed. The incident waves were broken on the approach slope or flat bed by its wave height. In the present study, all waves acting on the large cylindrical structure were limited to breaking bore after wave breaking. The effects of the position of the structure and the incident wave height on the wave force and wave transformations were mainly investigated with the concern of wave breaking. Further, the relations between the variation of wave energy by wave propagation after wave breaking and wave force acting on the structure were discussed to give the understanding of the full-linear wave-structure interactions in three-dimensional wave fields.

Nonhydrostatic Effects on Convectively Forced Mesoscale Flows (대류가 유도하는 중규모 흐름에 미치는 비정역학 효과)

  • Woo, Sora;Baik, Jong-Jin;Lee, Hyunho;Han, Ji-Young;Seo, Jaemyeong Mango
    • Atmosphere
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    • v.23 no.3
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    • pp.293-305
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    • 2013
  • Nonhydrostatic effects on convectively forced mesoscale flows in two dimensions are numerically investigated using a nondimensional model. An elevated heating that represents convective heating due to deep cumulus convection is specified in a uniform basic flow with constant stability, and numerical experiments are performed with different values of the nonlinearity factor and nonhydrostaticity factor. The simulation result in a linear system is first compared to the analytic solution. The simulated vertical velocity field is very similar to the analytic one, confirming the high accuracy of nondimensional model's solutions. When the nonhydrostaticity factor is small, alternating regions of upward and downward motion above the heating top appear. On the other hand, when the nonhydrostaticity factor is relatively large, alternating updraft and downdraft cells appear downwind of the main updraft region. These features according to the nonhydrostaticity factor appear in both linear and nonlinear flow systems. The location of the maximum vertical velocity in the main updraft region differs depending on the degrees of nonlinearity and nonhydrostaticity. Using the Taylor-Goldstein equation in a linear, steady-state, invscid system, it is analyzed that evanescent waves exist for a given nonhydrostaticity factor. The critical wavelength of an evanescent wave is given by ${\lambda}_c=2{\pi}{\beta}$, where ${\beta}$ is the nonhydrostaticity factor. Waves whose wavelengths are smaller than the critical wavelength become evanescent. The alternating updraft and downdraft cells are formed by the superposition of evanescent waves and horizontally propagating parts of propagating waves. Simulation results show that the horizontal length of the updraft and downdraft cells is the half of the critical wavelength (${\pi}{\beta}$) in a linear flow system and larger than ${\pi}{\beta}$ in a weakly nonlinear flow system.

Responses of Burning Liquid Propellant Sprays Perturbed by Unstable Pressure Waves (불안정한 압력파동 섭동에 의한 액체추진제 분무연소 반응)

  • Ko, Hyun;Lee, Gil-Yong;Yoon, Eung-Sub
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 1998.10a
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    • pp.3-3
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    • 1998
  • 액체추진제 로켓엔진 연소실에는 고유모드에 대응하는 음향파동이 내재되며 이러한 음향파동은 연소와의 상호작용을 통하여 불안정한 음향에너지를 공급받아 증폭되며 결국에는 연소불안정 상태에까지 이르게 된다. 이와 같은 불안정한 상태에 이르기 위해서는 연소로부터 되먹임되는 불안정 에너지의 양이 충분히 크고 구동 음향파동에 근접한 위상을 가져야 한다. 이와 같은 구동 메커니즘을 구성하는 상세한 물리적 현상들을 규명하고 예측하기 위한 많은 연구들이 보고되었으며, 이들 중 이론적인 시간 지연 모델을 사용하는 음향적인 방법은 매우 경제적인 반면 연소 현상에 대한 상세한 모사가 생략되어 연소 불안정의 구체적인 원인을 규명하는데 어려움이 있고, 파동 방정식에 의하여 연소실 내부의 파동 에너지 증가를 예측하는 방법은 연소기 내에서의 연소 메커니즘에 대한 고려 없이 연소에 의해 발생하는 에너지만을 포함하는 단점과 선형적인 연소 불안정에만 제한된다는 제한이 있다. 음향장과 커플된 기화반응 모델은 분무액적의 기화 과정이 추진제 연소의 지배과정이라는 가정 하에 연소응답을 기화반응으로 대체하는 방법으로, 역시 단시간 내에 결과를 얻을 수 있다는 장점이 있으나 기화반응으로부터 음향파동으로의 에너지 되먹임 과정이 배제되어 있어 정확한 결과를 구하기는 어렵다. 이에 대하여 최근에는 전산 모사적인 방법을 사용하는 대규모의 연소장 해석이 가능하여 짐으로써 음향파동에 의한 외란과 에너지 되먹임과정을 모두 포하마여 수치적인 방법을 사용하여 계산하는 액체추진제 로켓엔진의 고주파 연소불안정 해석방법들이 제시되고 있다.안정성 모드가 있음을 보였다. 밀도 변화가 있는 경우나 밀도 변화가 없는 경우 모두 sinuous 모드의 가장 불안정한 모드가 varicose 모드의 가장 불안정한 모드보다 더 불안정함을 보여주어 후류 유동은 자유 유동에 가까운 위상 속도를 가지는 sinuous 모드에 의해 지배될 것임을 예측할 수 있다. 연소반응이 완전연소에 가까울수록 그리고 압축성 효과가 클수록 유동내부의 온도가 증가하고 점성 또한 증가하여 후류유동은 안정됨을 알 수 있었다 유동변수들의 contour로부터 유동의 특성을 예측한 결과 baroclinic 항이 dilatational 항보다 상대적으로 크며, 중심선 상하에 생기는 vortex를 더욱 성장시킬 것으로 생각된다.냉각 홀의 막임, 연소 입자의 점착 부위 등을 예측하여 보완책을 준비할 수 있도록 하였다.$mm^2$sec였으며, 이는 다른 graphite/epixy 복합재의 확산계수와 유사한 값을 나타내고 있다. 또한 추진제가 충전된 연소관을 절단하여 밀폐한 후 95%RH 습도 조건에 보관함으로써 연소관 내부의 추진제 기계적 특성에 미치는 침투된 습기의 영향도 함께 고찰하였다. 추진제에 따라 차이는 있겠으나 추진제가 충전된 연소관은 순수 복합재 연소관에 비해 습기의 투과 정도가 작으며, 본 연소관에 충전된 RDX/AP계 추진제의 경우 추진제의 습기투과에 의한 추진제 물성 변화는 미미한 것으로 나타났다.의 향상으로, 음성개선에 효과적이라고 사료되었으며, 이 방법이 편측 성대마비 환자의 효과적인 음성개선의 치료방법의 하나로 응용될 수 있으리라 생각된다..

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Numerical Simulation of a Near shore Tsunami Using a Digital Wave Tank Simulation Technique (디지털 수치수조 기법에 의한 연안 Tsunami의 수치 시뮬레이션)

  • 박종천;전호환
    • Journal of Ocean Engineering and Technology
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    • v.17 no.6
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    • pp.7-15
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    • 2003
  • A Digital Wave Tank simulation technique, based on a finite-difference method and a modified marker-and-cell (MAC) algorithm, is applied in order to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach, Ohkushiri Island, and to predict maximum wove run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain, and the boundary values are updated at each time step, by a finite-difference time-marching scheme in the frame of the rectangular coordinate system. The fully nonlinear, kinematic, free-surface condition is satisfied by the modified marker-density function technique. The near shore Tsunami is assumed to be a solitary wave, and is generated from the numerical wave-maker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods, based on the shallow-water wave theory.

Low-pass Filters for Removing Numerical Noises of Boussinesq Equation Model (Boussinesq 방정식 모델의 수치잡음 제거를 위한 저파수 통과 필터에 대한 고찰)

  • Chun, In-Sik;Sim, Jae-Seol
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.19 no.5
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    • pp.418-428
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    • 2007
  • In the calculation of wave propagation by Boussinesq equation model, it is very common to experience numerical noises generated from nonlinear interaction and breaking wave occurrence, and the numerical solution is rapidly diverged unless the noises are properly controlled. A comparative study was here undertaken for the characteristics of three different lowpass filters (FFT filter, Gaussian filter and Shapiro filter) which are all designed to be applied to the interim results of numerical calculation. The numerical results obtained with application of respective filter techniques were compared with the results of an existing hydraulic experiment for the aspects of noise suppression, conservation of main signal and altering time. The results show that the Shapiro filter can be best applied with optimal choices of its element number, pass number and filtering tune interval. The combination of the number of filter element off, pass number of 50 or less, and application interval of 100 to 200 time steps generally showed good performance in both accuracy and efficiency of the numerical calculation.