• Title/Summary/Keyword: Difference equation

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Prediction of Excess Pore Water Pressure of Reservoir Embankment on Soft Ground (연약지반상에 축조된 저수지 제방의 과잉공극수압 예측)

  • Min, Hag-Gyou;Lee, Dal-Won
    • Journal of The Korean Society of Agricultural Engineers
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    • v.50 no.2
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    • pp.37-44
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    • 2008
  • A theoretical equation was proposed to consider the effect of ponding for the excess pore water pressure in agricultural reservoir on soft clay ground. The value of excess pore water pressure predicted using the proposed equation was compared to those predicted with the Terzaghi's method and the finite difference method(FDM), respectively, for the purpose of verification. The degree of consolidation according to ponding predicted by applying the proposed equation was close to the observed degree of consolidation on the double drainage condition(at DP-3) but it was less than the observed degree of consolidation on the single drainage condition(at DP-5). The equation was very applicable to practice because the analysis result by the equation was close to the observed data.

A Calculation of 1 Dimensional Blasting Pressure Uslng the Flux-Corrected Transport Algorithm (Flux-Corrected Transport Algorithm을 적용한 1차원 발파압력산정에 관한 연구)

  • 김문겸;오금호;이필규
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1995.10a
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    • pp.76-83
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    • 1995
  • Estimation of blasting behavior of explosives is prerequisite in the numerical analysis of blasting works. In this study, blasting pressure is estimated by the finite difference method using the Flux-Corrected Transport Algorithm. To formulate the behavior of blasting gas, the mass conservation equation, the moment conservation equation, the energy conservation equation and the ideal gas state equation are used. The simplified species conservation equation is included to simulate the behavior of reacting explosives. To verify the calculation, the Sod's shock tube problem, the strong shock problem and the reacting problem we used. Numerical results show that the shock wave can be captured by means of the FCT algorithm in the reacting and nonreacting states.

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A Numerical Model for Cohesive Suspended Load Movement (점착성 부유사 이동에 관한 수치모형)

  • 안수한;이상화
    • Water for future
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    • v.23 no.1
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    • pp.119-127
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    • 1990
  • The concentration of cohesive suspended sediment is determined by the circulation of water and the material dispersion. The equations of the two-dimensional, depth-integrated dispersive transport are the Reynolds equation, continuity equation, and advection-dispersion equation based on the Fick's law. A finite difference method has been applied to two models of circulation and dispersion transport. The circulation model is solved by the explicit scheme and the dispersion transport model is solved by multi-operational scheme. It is investigated wheter advective terms are included when the equation of circulation is applied to the model. For advection-dispersion equation, it was also investigated about variations of suspended sediment concentration with respect to the critical shear stresses.

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Numerical Analysis of Cavitation Flow Around Hydrofoils (3차원 수중익형 주위의 캐비테이션 유동 전산해석)

  • Kim, S.H.;Koo, T.K.;Park, W.G.;Kim, D.H.
    • The KSFM Journal of Fluid Machinery
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    • v.11 no.3
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    • pp.7-13
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    • 2008
  • The cavitating flow simulation is of practical importance for many engineering systems, such as pump, turbine, nozzle, Infector, etc. In the present work, a solver for two-phase flows has been developed and applied to simulate the cavitating flows past hydrofoils. The governing equation is the two-phase Navier-Stokes equation, comprised of the continuity equation of liquid and vapor phase. The momentum and energy equation is in the mixture phase. The solver employs an implicit, dual time, preconditioned algorithm using finite difference scheme in curvilinear coordinates. An experimental data and other numerical data were compared with the present results to validate the present solver. It is concluded that the present numerical code has successfully accounted for two-phase Navier-Stokes model of cavitation flow.

Implementation and Experiments of Sparse Matrix Data Structure for Heat Conduction Equations

  • Kim, Jae-Gu;Lee, Ju-Hee;Park, Geun-Duk
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.12
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    • pp.67-74
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    • 2015
  • The heat conduction equation, a type of a Poisson equation which can be applied in various areas of engineering is calculating its value with the iteration method in general. The equation which had difference discretization of the heat conduction equation is the simultaneous equation, and each line has the characteristic of expressing in sparse matrix of the equivalent number of none-zero elements with neighboring grids. In this paper, we propose a data structure for sparse matrix that can calculate the value faster with less memory use calculate the heat conduction equation. To verify whether the proposed data structure efficiently calculates the value compared to the other sparse matrix representations, we apply the representative iteration method, CG (Conjugate Gradient), and presents experiment results of time consumed to get values, calculation time of each step and relevant time consumption ratio, and memory usage amount. The results of this experiment could be used to estimate main elements of calculating the value of the general heat conduction equation, such as time consumed, the memory usage amount.

A Comparison of the Goodness-of-Fit between Two Models of Expenditure Function: a Single-Equation Model versus a Complete- System-of-Demand-Equation Model (단일방정식과 관련방정식체계를 적용한 소비지출 함수의 모델 적합성 비교)

  • 황덕순;김숙향
    • Journal of Families and Better Life
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    • v.20 no.1
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    • pp.45-56
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    • 2002
  • The main purposes of this article are to introduce the theoretical backgrounds and empirical application methods of two different Models for the function of expenditure, and to compare the goodness-o(-fit of the two models: a single-equation model and a complete-system-of-demand-equation model. For the empirical analysis of the single-equation model, a linear formula and a double-leg formula were employed. In order to test the complete-system-of-demand-equation model empirically, the \"Linear Approximation/Almost Ideal Demand System (LA/AIDS)" was used. The independent variables were the total living expense and expenditure categories Price index. The data used in this study were obtained from the quarterly statistics of "The Annual Report on the Urban Family Income and Expenditure Survey (Dosigagyeyonbo)" and "The Annual Report on the Consumer Price Index (Sobijamulgajaryo)," for the years 1994 to 1997. The goodness-of-fit (R-square) was higher with the complete-system-of-demand-equation model than with the single-equation model for the budget share on food (excluding eating-out expenses) and for the share on cultural and recreational activities. However, there was no difference between the two models in terms of the proportion of the expenditure on automobile fuel.fuel.

A Study on Consistency of Numerical Solutions for Wave Equation (파동방정식 수치해의 일관성에 관한 연구)

  • Pyun, Sukjoon;Park, Yunhui
    • Geophysics and Geophysical Exploration
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    • v.19 no.3
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    • pp.136-144
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    • 2016
  • Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

Steady-State Current Characteristics for Squirrel Cage Induction Motor according to Design Variables of Rotor Bars using Time Difference Finite Element Analysis

  • Kim, Young Sun
    • Journal of Magnetics
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    • v.22 no.1
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    • pp.104-108
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    • 2017
  • Induction motors have wide applicability in many fields, both in industrial sectors and households, for their advantages of a high efficiency and robust structure. The introduction of power-source-containing harmonics into the induction motor winding lowers its efficiency and increases its temperature, greatly affecting its operation characteristics. In this study, we performed an electromagnetic field analysis using the time-difference finite-element method with the purpose of analyzing the steady-state current characteristics of an induction motor. Additionally, we calculated the steady-state current with a method combining an electromagnetic field equation and a circuit equation. In the electromagnetic field analysis, the nonlinearity was taken into account using the Newton-Raphson method, and a backward time-difference method was employed for the time derivative term. Then, we compared the steady-state current of the induction motor obtained by calculation with the experimentally measured values, thus validating the proposed algorithm. Furthermore, we analyzed the impacts of the shape and material of the rotor conductor bar of the induction motor on the steady-state current of the main winding.