• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.813-829
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• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• Journal of Ship and Ocean Technology
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• 제5권4호
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• pp.29-43
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• 2001

In this paper, free surface flows around an advancing two-dimensional rectangular cylinder piercing the free surface are studied using numerical and experimental methods. Especially, wave breaking phenomenon around the cylinder is treated in detail. A series of numerical simulations and experiments were performed for the purpose of comparison. For the numerical simulations, a finite difference method was adopted with a rectangular grid system, and the variation of the free surface was computed by the marker density method. The computational results are compared with the experiments. It is confirmed that the present numerical method is useful for the numerical simulation of nonlinear free surface waves around a piercing body.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Geomechanics and Engineering
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• 제12권6호
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• pp.1003-1020
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• 2017

Estimation of groundwater inflow into underground opening is of critical importance for the design and construction of underground structures. Groundwater inflow into a pilot underground storage facility in China was estimated using analytical equations, numerical modeling and field measurement. The applicability of analytical and numerical methods was examined by comparing the estimated and measured results. Field geological investigation indicated that in local scale the high groundwater inflows are associated with the appearance of open joints, fractured zone or dykes induced by shear and/or tensile tectonic stresses. It was found that 8 groundwater inflow spots with high inflow rates account for about 82% of the total rate for the 9 caverns. On the prediction of the magnitude of groundwater inflow rate, it was found that could both (Finite Element Method) FEM and (Discrete Element Method) DEM perform better than analytical equations, due to the fact that in analytical equations simplified assumptions were adopted. However, on the prediction of the spatial distribution estimation of groundwater inflow, both analytical and numerical methods failed to predict at the present state. Nevertheless, numerical simulations would prevail over analytical methods to predict the distribution if more details in the simulations were taken into consideration.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2006년도 Asia Navigation Conference
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• pp.157-165
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• 2006

In February,2004, at International Maritime Organization (IMO), LONDON, a new international convention 'International Convention fur the Control and Management of Ship's Ballast Water and Sediment 2004' was adopted. It is called 'Ballast Water Management Convention (BWM)'. Ballast water means charged seawater or fresh water in ship's special tanks (ballast tank) to keep safety navigation and ship's maneuverability. However, from 1980, it was point out the serious problem for marine ecosystem and human life that ballast water includes harmful marine species (and small organisms) and these species are also discharged along with ballast water. These species were released with discharged ballast water in water areas, where species are different from discharged ballast water. The problem is that released species increase when released species are more powerful than native species and consequently, marine ecological system is destroyed in released water area. Authors have inspected the validity of the ballast water exchange using pumping-through method that is one of the methods of ballast water management. In this paper, the numerical simulation of the motion and density of the fluid at the time of exchange of the fluid in a 2-dimensional tank using the pumping-through method was carried out by using two different type numerical methods. One method is MPS method that is one of the particle methods. Other one is Finite Different Method (FDM). Authors were compared with result of two numerical method calculations and experiment result and reported some knowledge from these results.

• 대한수학회보
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• 제28권2호
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• pp.207-217
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• 1991

• 터널과지하공간
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• 제21권2호
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• pp.128-137
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• 2011

수직 시추공에 대한 일반적인 수압파쇄시험으로부터 구해지는 균열폐쇄압력은 암반의 최소수평주응력을 직접 나타내기 때문에 현지암반의 응력분포양상을 해석하는데 있어서 매우 중요한 요소이다. 그러나 수압파쇄균열의 거동과 현지암반의 응력분포양상의 관계로 인하여 대부분의 경우 이 균열폐쇄압력은 수압파쇄 압력이력곡선 상에서 애매모호한 값으로 나타난다. 본 연구에서는 수압파쇄시험으로부터 균열폐쇄압력을 산정하기 위하여 여러 연구자들에 의해 제안된 기법들의 특성을 비교해 보고자 수치해석을 실시하였다. 즉, 유체의 가압에 의한 암반 내 균열의 발생이라는 수압파쇄의 특성을 모사하기 위하여 H-M couple 해석을 적용하였으며, 또한 수치해석 모델의 형상학적 특성에 따른 균열의 전파양상을 검토하기 위해 4가지 서로 다른 형태의 요소망을 구축하여 해석을 실시하였다. 각각의 요소망에 대한 수치해석 결과, 그래픽 방법이 통계적 방법에 비해 상대적으로 낮은 수준의 균열폐쇄압력을 보였으며, 따라서 시험공 주변에서의 응력 이상대의 존재 및 복잡한 메커니즘을 수반하는 수압파쇄균열의 발생양상을 감안할 때 수압파쇄시험에 의한 균열폐쇄압력의 산정시 특별한 주의가 요구된다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 추계 학술대회논문집
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• pp.9-14
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• 2000

Computational methods can be classified roughly into two parts: one is the methods based on a potential flow theory, and the other is numerical solvers(CFD) based on Navier-Stockes equation. Methods based on a potential theory are more effective than CFD when the free surface effect is considered. Especially Rankine source method seems to become widespread for simulations of wave making problems. For computations of viscous flow problems, CFD techniques have rapidly been developed and have shown many successful results in the viscous flow calculation. Present paper introduces a computational system 'WAVIS' which includes a pre-processor, potential ant viscous flow solvers and a post-processor. To validate the system, the calculated results for modem commercial hull forms are compared with measurements. It is found that the results from the system are in good agreement with the experimental data, illustrating the accuracy of the numerical methods employed for WAVIS.

• 대한기계학회논문집B
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• 제21권2호
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.

• Korea-Australia Rheology Journal
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• 제18권2호
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• pp.91-98
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• 2006

We compare FT (Fourier Transform) and SD (Stress Decomposition), the interpretation methods for LAOS (Large Amplitude Oscillatory Shear). Although the two methods are equivalent in mathematics. they are significantly different in numerical procedures. Precision of FT greatly depends on sampling rate and length of data because FT of experimental data is the discrete version of Fourier integral theorem. FT inevitably involves unnecessary frequencies which must not appear in LAOS. On the other hand, SD is free from the problems from which FT suffers, because SD involves only odd harmonics of primary frequency. SD is based on two axioms on shear stress: [1] shear stress is a sufficiently smooth function of strain and its time derivatives; [2] shear stress satisfies macroscopic time-reversal symmetry. In this paper, we compared numerical aspects of the two interpretation methods for LAOS.