• Title, Summary, Keyword: numerical solutions

### NUMERICAL SOLUTIONS OF AN IMPACT OF NATURAL CONVECTION ON MHD FLOW PAST A VERTICAL PLATE WITH SUCTION OR INJECTION

• Ambethkar, V.
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.201-202
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• 2008
• Because of the importance of suction or injection in the fields of aerodynamics, space science and many other industrial applications, our present study is motivated. The effect of natural convection on MHD flow past a vertical plate with suction or injection is studied. We have tried to solve the dimensionless governing equations by using finite difference scheme. To ensure the validity of our numerical solutions, we have compared our numerical solutions for temperature and velocity for the case of suction and injection for unit Prandtl number with the available exact solutions in the literature. The corresponding codes were written in Mathematica 5.0 for calculating numerical solutions for temperature and velocity and the comparison between the exact and numerical solutions. For the purpose of discussing the results some numerical calculations are carried out for non-dimensional temperature T, velocity u, skin friction ${\tau}$ and the Nusselt number $N_u$, by making use of it, the rate of heat transfer is studied.

### Comparison of a Groundwater Simulation-Optimization Numerical Model with the Analytical Solutions (해안지하수개발 최적화수치모델과 해석해의 비교연구)

• Shi, Lei;Cui, Lei;Lee, Chan-Jong;Park, Nam-Sik
• Proceedings of the Korea Water Resources Association Conference
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• pp.905-908
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• 2009
• In the management of groundwater in coastal areas, saltwater intrusion associated with extensive groundwater pumping, is an important problem. The groundwater optimization model is an advanced method to study the aquifer and decide the optimal pumping rates or optimal well locations. Cheng and Park gave the analytical solutions to the optimization problems basing on Strack's analytical solution. However, the analytical solutions have some limitations of the property of aquifer, boundary conditions, and so on. A simulation-optimization numerical method presented in this study can deal with non-homogenous aquifers and various complex boundary conditions. This simulation-optimization model includes the sharp interface solution which solves the same governing equation with Strack's analytical solution, therefore, the freshwater head and saltwater thickness should be in the same conditions, that can lead to the comparable results in optimal pumping rates and optimal well locations for both of the solutions. It is noticed that the analytical solutions can only be applied on the infinite domain aquifer, while it is impossible to get a numerical model with infinite domain. To compare the numerical model with the analytical solutions, calculation of the equivalent boundary flux was planted into the numerical model so that the numerical model can have the same conditions in steady state with analytical solutions.

### Sensitivity of Numerical Solutions to Time Step in a Nonlinear Atmospheric Model (비선형 대기 모형에서 수치 해의 시간 간격 민감도)

• Lee, Hyunho;Baik, Jong-Jin;Han, Ji-Young
• Journal of the Korean earth science society
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• v.34 no.1
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• pp.51-58
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• 2013
• An appropriate determination of time step is one of the important problems in atmospheric modeling. In this study, we investigate the sensitivity of numerical solutions to time step in a nonlinear atmospheric model. For this purpose, a simple nondimensional dynamical model is employed, and numerical experiments are performed with various time steps and nonlinearity factors. Results show that numerical solutions are not sensitive to time step when the nonlinearity factor is not influentially large and truncation error is negligible. On the other hand, when the nonlinearity factor is large (i.e., in a highly nonlinear regime), numerical solutions are found to be sensitive to time step. In this situation, smaller time step increases the intensity of the spatial filter, which makes small-scale phenomena weaken. This conflicts with the fact that smaller time step generally results in more accurate numerical solutions owing to reduced truncation error. This conflict is inevitable because the spatial filter is necessary to stabilize the numerical solutions of the nonlinear model.

### NUMERICAL SOLUTIONS FOR SPACE FRACTIONAL DISPERSION EQUATIONS WITH NONLINEAR SOURCE TERMS

• Choi, Hong-Won;Chung, Sang-Kwon;Lee, Yoon-Ju
• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010
• Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

### Numerical algorithm with the concept of defect correction for incompressible fluid flow analysis (오차수정법을 도입한 비압축성 유체유동 해석을 위한 수치적 방법)

• Gwon, O-Bung
• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.341-349
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• 1997
• The characteristics of defect correction method are discussed in a sample heat conduction problem showing the numerical solution of the error correction equation can predict the error of the numerical solution of the original governing equation. A way of using defect correction method combined with the existing algorithm for the incompressible fluid flow, is proposed and subsequently tested for the driven square cavity problem. The error correction equations for the continuity equation and the momentum equations are considered to estimate the errors of the numerical solutions of the original governing equations. With this new approach, better velocity and pressure fields can be obtained by correcting the original numerical solutions using the estimated errors. These calculated errors also can be used to estimate the orders of magnitude of the errors of the original numerical solutions.

### Numerical Solutions of Third-Order Boundary Value Problems associated with Draining and Coating Flows

• Ahmed, Jishan
• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.651-665
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• 2017
• Some computational fluid dynamics problems concerning the thin films flow of viscous fluid with a free surface and draining or coating fluid-flow problems can be delineated by third-order ordinary differential equations. In this paper, the aim is to introduce the numerical solutions of the boundary value problems of such equations by variational iteration method. In this paper, it is shown that the third-order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration method. These solutions are gleaned in terms of convergent series. Numerical examples are given to depict the method and their convergence.

### NUMERICAL SOLUTION FOR ROBOT ARM PROBLEM USING LIMITING FORMULAS OF RK(7,8)

• Senthilkumar, S.
• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.793-809
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• 2008
• The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the RK-eight stage seventh order limiting formulas. The parameters governing the arm model of a robot control problem have also been discussed through RK-eight stage seventh order limiting algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. Based on the numerical results a thorough comparison is carried out between the numerical algorithms.

### Verification of the Contaminant Transport Numerical Model in Subsurface Soil (토양내 오염물이동 수치모델 검증)

• Suh, Kyung-Suk;Kim, Eun-Han;Han, Moon-Hee;Lee, Chang-Woo
• Journal of Radiation Protection and Research
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• v.27 no.1
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• pp.67-75
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• 2002
• The groundwater flow and contaminant transport numerical models have been established for understanding the movement of pollutants in surface soil environment. The numerical solutions were compared with the analytic solutions for the verification and the application of the models. The numerical solutions from the groundwater and transport models agreed welt with analytic solutions. Especially, the results of groundwater flow model were validated in one- and two-dimensional heterogeneous media. Therefore, it will represent well the characteristics of the heterogeneous media in the field applications. Also, the phenomena of the pollutant dispersion represented quite well by the advection and the hydrodynamic dispersion in the results of the transport model. The important input factor is the choice of complicated boundary conditions in operating the numerical models. The numerical results are influenced by the choice of the proper boundary conditions.

### A Theoretical Study on the Analytical Solutions for Laterally Loaded Pile (횡방향 하중을 받는 말뚝의 해석해에 대한 이론적 고찰)

• Lee, Seung-Hyun
• Journal of Korean Society of Hazard Mitigation
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• v.11 no.3
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• pp.111-116
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• 2011
• Analytical solutions for laterally loaded piles were derived. Critical pile length which can be considered as the length for behaving as long pile was investigated varying with densities of sandy soils. Lateral behaviors obtained from analytical solution and numerical solution were also investigated. Non-dimensional critical pile lengths obtained from analytical solutions for three types of pile head boundary conditions were 2.3~3.2. By comparing analytical solutions with numerical solutions, distribution of pile deflection and that of moment were similar and it can be seen that pile head deflection obtained by analytical method is conservative. And the values of moments were not too different between analytical solution and numerical solution.

### Closed Form Inverse Kinematic Solutions for General Combination of Three-Joint Manipulator (3관절 매니퓰레이터의 일반적 조합에 대한 역기구학적 폐형해)

• 한규범
• Proceedings of the Korean Society of Precision Engineering Conference
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• pp.363-368
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• 1995
• A general method of solving inverse kinematics of three-joint manipulator composed of revolute joints or prismatic joints or combinations of those joints is presented in this study. In completing real-time control, it is very important to obtain the closed form solutions of inverse kinematics rather than iterative numerical solutions, because iterative numerical solutions are generally much slower than the corresponding closed form solutions. If it is possible to obtain the inverse kinematic solutions for general cases of considering twist anlges and offsets, the manipulator work space can be designed and enlarged more effciently for specific task. Moreover, in idustrial manipulators, the effect of main three joints is larger than that of the other three joints related to orientation in the view of work space. Therfore the solutions of manin three-joint are considered. Even The inverse kinematic equations are complicatedly coupled, the systematical solving process by using symbolic calculation is presented.