• Coupled systems mechanics
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• v.8 no.2
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• pp.129-146
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• 2019

The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Journal of Environmental Health Sciences
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• v.31 no.6
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• pp.489-497
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• 2005

A numerical method for the mathematical water modeling in 2-dimensional flow has been developed. The model based on a split operator technique, in which, the advection term is calculated using the upwind scheme. The diffusion term is one- dimensionalized and calculated using Crank-Nicholson's implicit finite difference scheme to reduce the numerical errors from large time steps and variable spacings. It also provides a relatively simple and economic method for more accurate simulation of pollutant dispersion. Water depths and flow velocities in the Boreyong reservoir during the normal water periods were predicted by numerical experiments with a 2-dimensional flow model so as to provide current field data for the study of advection and diffusion of pollutants. Developed 2-dimensional water quality model is applied to Boreyong reservoir to simulate a spatial and periodical changes of water quality.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.537-555
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• 2023

In this paper, we consider two types of fractional boundary value problems, one of them is an implicit type and the other will be an integro-differential type with nonlocal integral multi-point boundary conditions in the frame of generalized Hilfer fractional derivatives. The existence and uniqueness results are acquired by applying Krasnoselskii's and Banach's fixed point theorems. Some various numerical examples are provided to illustrate and validate our results. Moreover, we get some results in the literature as a special case of our current results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.3 no.1
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• pp.13-24
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• 1983

A mathematical model for the two-dimensional unsteady flow was developed by introducing Abbott's implicit finite difference operator and double sweep algorithm, which could be applied to simulate the respose of a harbor against the intrusion of long waves through the entrance connected to open sea. In order to improve its accuracy corresponding to the field phenomena, bottom resistance, Coriolis force, wind effect terms were included and wave direction and radiating effect was considered. The result of seiche test was always stable and the amplitude was accurate. Some phase shift was occured, but it could be reduced by using small values of Courant number and many points per a wave length as well. A comparision with the Ippen and Goda's theoritical and hydraulic experimental works was fulfilled.

• Journal of KIISE:Software and Applications
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• v.26 no.8
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• pp.1010-1017
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• 1999

불완전한 계획 영역 이론은 오류 영역(noisy domain)에서 하나의 상태에 상반된 연산자들이 적용되는 불일치성 문제를 야기할 수 있다. 이 문제를 해결하기 위해서 본 논문은 상태를 기술하기 위해 다치 논리를 도입하여 제어지식으로서의 부정적 선행조건을 학습하는 새로운 방법을 제안한다. 기계에는 알려지지 않은 이러한 제어지식이 인간에게는 반대개념으로 잠재적으로 사용되고 있다. 이러한 잠재된 개념을 학습하기 위해 본 논문은 반대 연산자들로 구성된 사이클을 영역이론으로부터 기계적으로 생성하고, 이 연산자들에 대한 실험을 통해 반대 리터럴(literal)들을 추출한다. 학습된 규칙은 불일치성을 방지하면서 동시에 중복된 선행조건을 제거하여 연산자를 단순화시킬 수 있다.Abstract An incomplete planning domain theory can cause an inconsistency problem in a noisy domain, allowing two opposite operators to be applied to a state. To solve the problem, we present a novel method to learn a negative precondition as control knowledge by introducing a three-valued logic for state description. However, even though the control knowledge is unknown to a machine, it is implicitly known as opposite concept to a human. To learn the implicit concept, we mechanically generate a cycle composed of opposite operators from a domain theory and extract opposite literals through experimenting the operators. A learned rule can simplify the operator by removing a redundant precondition while preventing inconsistency.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.685-692
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• 2003

A numerical simulation of flame propagation in a micro combustor was carried out. Combustor has a sub -millimeter depth cylindrical internal volume and axisymmetric one-dimensional was used to simplify the geometry. Semi-empirical heat transfer model was used to account for the heat loss to the walls during the flame propagation. A detailed chemical kinetics model of $H_2/Air$ with 10 species and 16 reaction steps was used to calculate the combustion. An operator-splitting PISO scheme that is non-iterative, time-dependent, and implicit was used to solve the system of transport equations. The computation was validated for adiabatic flame propagation and showed good agreement with existing results of adiabatic flame propagation. A full simulation including the heat loss model was carried out and results were compared with measurements made at corresponding test conditions. The heat loss that adds its significance at smaller value of combust or height obviously affected the flame propagation speed as final temperature of the burnt gas inside the combustor. Also, the distribution of gas properties such as temperature and species concentration showed wide variation inside the combustor, which affected the evaluation of total work available of the gases.

• Journal of the Korea Computer Graphics Society
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• v.22 no.5
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• pp.1-16
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• 2016

In this paper, we propose and efficient curve reconstruction method based on the classical least-square fitting scheme. Specifically, given planar sample points equipped with normals, we reconstruct the objective curve as the zero set of a hierarchical implicit ZP(Zwart-Powell)-spline that can recover large holes of dataset without loosing the fine details. As regularizers, we adopted two: a Tikhonov regularizer to reduce the singularity of the linear system and a discrete Laplacian operator to smooth out the isocurves. Benchmark tests with quantitative measurements are done and our method shows much better quality than polynomial methods. Compared with the hierarchical bi-quadratic spline for datasets with holes, our method results in compatible quality but with less than 90% computational overhead.