• Title/Summary/Keyword: Pseudospectral Method

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The Modeling and Simulation for Pseudospectral Time-Domain Method Synthetic Environment Underwater Acoustics Channel applied to Underwater Environment Noise Model (수중 환경 소음 모델이 적용된 의사 스펙트럼 시간영역 법 합성환경 수중음향채널 모델링 및 시뮬레이션)

  • Kim, Jang-Eun;Kim, Dong-Gil;Han, Dong-Seog
    • Journal of the Korea Society for Simulation
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    • v.25 no.3
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    • pp.15-28
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    • 2016
  • It is necessary to analyze underwater acoustics channel(UAC) modeling and simulation for underwater weapon system development and acquisition. In order to analyze UAC, there are underwater acoustics propagation numerical analysis models(Ray theory, Parabolic equation, Normal-mode, Wavenumber integration). However, If these models are used for multiple frequency signal analysis, they are inaccurate to calculate result of analysis effectiveness and restricted for signal processing and analysis. In this paper, to overcome this problem, we propose simple/multiple frequency signal analysis model of the Pseudospectral Time-Domain Method synthetic environment UAC applied to underwater environment noise model as like as realistic underwater environment. In order to confirm the validation of the model, we performed the 9 scenarios simulation(4 scenarios of single frequency signal, 4 scenarios of multiple frequency signal, 1 scenario of single/multiple frequency signal like submarine radiated noise) for validation and confirmed the validation of this model through the simulation model.

NEW ALGORITHMS FOR SOLVING ODES BY PSEUDOSPECTRAL METHOD

  • Darvishi, M.T.
    • Journal of applied mathematics & informatics
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    • v.7 no.2
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    • pp.439-451
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    • 2000
  • To compute derivatives using matrix vector multiplication method, new algorithms were introduced in [1.2]n By these algorithms, we reduced roundoff error in computing derivative using Chebyshev collocation methods (CCM). In this paper, some applications of these algorithms ar presented.

Numerical Models for Atmospheric Diffusion Problems by Pseudospectral Method (1) - Atmospheric Diffusion Equations and Spectral Model - (의사스펙트로법에 의한 대기확산형상의 수치모델(1) - 대기확산방정식과 스펙트로모델 -)

  • 김선태;장영기
    • Journal of Korean Society for Atmospheric Environment
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    • v.7 no.3
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    • pp.189-196
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    • 1991
  • In recent years spectral methods have been found to be a powerful tool for the numerical solution of hynamic differential equations. The main attraction of spectral method is accuracy even though it is generally difficult to implement and solve the complex problems using spectral method. We introduced diffusion equations describing the state of air pollution and solved by pseutospectral method in dimensionless form. The results were compared with both those of other numerical methods and analytical solutions. Comparing with finite difference method and finite element method, spectral method shows the highest accuracy for one dimension problem in this study. Also, the results of two dimensional diffusion problems show good agreement with analytical solutions.

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A Comparison of Numerical Methods for the Advection Equation for Air Pollution Models (대기오염모델에서의 이류방정식에 대한 수치적 방법의 비교)

  • 심상규;박영산
    • Journal of Korean Society for Atmospheric Environment
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    • v.8 no.3
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    • pp.162-168
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    • 1992
  • Numerical solutions to the advection equations used for long-range transport air pollution models are calculated using three numerical methods; Antidiffusion correction method(Smolarkiewicz, 1983), Positive definite advecton scheme obtained by nonlinear renormalization of the advective fluxes(Bott, 1989), and Positive definite pseudospectral method(Bartnicki, 1989). Accuracy, numerical diffusion and computational time requirement are compared for two-dimensional transport calculations in a uniform rotational flow field. The solutions from three methods are positive definite. Bartnicki(1989)'s method is most conservative but requires approximately 10 times as much computational time as Smolarkiewicz(1983)'s method of which numerical diffusion is the largest. All three methods are more conservative for a cone shape initial condition than for a rectangular block initial condition with a steep gradient.

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Generalized Computational Nodes for Pseudospectral Methods

  • Kim, Chang-Joo;Park, Soo Hyung;Jung, Sung-Nam;Sung, Sangkyung
    • International Journal of Aeronautical and Space Sciences
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    • v.15 no.2
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    • pp.183-189
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    • 2014
  • Pseudo-spectral method typically converges at an exponential rate. However, it requires a special set of fixed collocation points (CPs) to get highly accurate formulas for partial integration and differentiation. In this study, computational nodes for defining the discrete variables of states and controls are built independently of the CPs. The state and control variables at each CP, which are required to transcribe an NOCP into the corresponding NLP, are interpolated, using those variables allocated at each node. Additionally, Lagrange interpolation and spline interpolation are investigated, to provide a guideline for selecting a favorable interpolation method. The proposed techniques are applied to the solution of an NOCP using equally spaced nodes, and the computed results are compared to those using the standard PS approach, to validate the usefulness of the proposed methods.

On the Most Unstable Disturbance of Channel Flows and Blasius Flow (관 유동과 Blasius 유동에서 가장 불안정한 교란에 관하여)

  • Choi, Sang-Kyu;Chung, Myung-Kyoon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.6
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    • pp.766-772
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    • 2003
  • The pseudospectral method for stability analysis was used to find the most influential disturbance mode for transition of plane channel flows and Blasius flow at their critical Reynolds numbers. A number of various oblique disturbance waves were investigated for their pseudospectra and resolvent norm contours in each flow, and an exhaustive search method was employed to find the disturbing waves to which the flows become most unstable. In plane Poiseuille flow an oblique disturbance with a wavelength of 3.59h (where h is the half channel width) at an angle $28.7^{\circ}$ was found to be the most influential for the flow transition to turbulence, and in plane Couette flow it is an oblique wave with a wavelength of 3.49h at an angle of $19.4^{\circ}$. But in Blasius flow it was found that the most influential mode is a normal wave with a wavelength of $3.44{\delta}_{999}$. These results imply that the most influential disturbance mode is closely related to the fundamental acoustic wave with a certain shear sheltering in the respective flow geometry.