Papers by Keyword: Numerical Solution

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Authors: Bo Wang, Jin Feng Mao, Li Jun Wang
Abstract: An analysis was carried out to study the performance of straight rectangular fin with the psychometric correlations given by Hyland and Wexler when subjected to simultaneous heat and mass transfer. Numerical solutions are obtained for the fin efficiency and 2-D temperature distribution with SOR method when the fin surface is dry, fully wet and partially wet. The result was compared with those of previous studies in released literature. The effect of fin parameters including the ratio of fin width and fin thickness to fin length as well as Bix on fin efficiency was also studied. It is found that the temperature distribution on the fin is really two-dimensional and the change of fin parameters shows impressive effect on fin efficiency and 2-D temperature distribution.
Authors: Jin Feng Mao, Bo Wang, Shi Bin Geng, Lu Yan Sui
Abstract: An analysis was carried out to study the efficiency of straight rectangular fin with combined heat and mass transfer. Numerical solutions are obtained for fin efficiency with SOR method when the fin surface is dry, fully wet and partially wet. The effect of fin parameters including the ratio of fin width and fin thickness to fin length as well as Bix on fin efficiency were also investigated. It is found that fin parameters shows impressive effect on 2-D fin efficiency, and the critical air relative humidity becomes closer to air saturated humidity when Bix increases.
Authors: Dan Ping Gui
Abstract: The FitzHugh-Nagumo equation is an important nonlinear reaction-diffusion equation used in physics and chemicals. To obtain the numerical solution of partial differential equations, the compact finite difference method is widely applied. In this paper, I propose a new numerical solution to FitzHugh-Nagumo equation by using a fourth-order compact finite difference scheme in space, and a semi-implicit Crank-Nicholson method in time. I further calculate the results in terms of accuracy by leveraging the proposed method and exact solution. In particular, I compare the new method whose convergence order is close to four with the second order central difference method. The simulated results show the new solution is more accurate and effective. The proposed method is expected to be a good solution to some problems in the real world.
Authors: Dong Yan Shi, Ku Ang Xia, Hua Chun Lin
Abstract: For the solutions to engineering equipment with pipes, unknown forces and unclear constraint conditions on the pipes result in the analysis limitation due to the high temperature and fluid pressure to pipes. In this paper, a new method for determining the loads is established to problems with many pipes. In the method, based on the combination of FEM and Successive Approximation Approach, pipes forces on the equipment are analyzed. By the analysis of suitable forces, the relationship between forces and stress can be obtained. The cycling process of “loading-solving-determining-adjusting” is carried out to approaching destinations based on hundreds of numerical results. Moreover, an evaluation scheme is built to evaluate groups of forces and guarantee equipment to work normally under some certain forces. The constraint condition from groups of forces can be also confirmed. A case study gave the verification of the method.
Authors: Xian Guo Han, Jun Zhang
Abstract: The fixed point iteration method was proposed to solve the forward kinematics of parallel kinematics mechanisms as a new method. In every iteration through the reverse kinematics the previous iteration intermediate position and posture determined stick orientation vectors. And the stick ports, which were obtained by multiplying stick orientation vectors and given stick lengths, determined the next iteration intermediate position and posture. The final position and posture satisfying the convergence conditions would be obtained. 6-SPS was taken as an example to verify that this method was available and correct. Compared with the Newton iteration, this method possesses more advantages, such as simpler formula, higher speed of the convergence, smaller program workload, and less influence of initial values on the convergence.
Authors: Wei Zhou, Qian Mu Li, Hong Zhang
Abstract: A method to get numerical solutions to Nonlinear Cyber-Security Equationss with the the N algorithm is proposed . This paper especially focused on its converging rate and application. Also, It did some comparison between with other universal algorithms. Both mathematical method and experimental method are used to do the comparison. This paper gave strict mathematical proof and also used the results we got from our program to draw a solid conclusion.
Authors: Li Hua Sun, En Liang Zhao, Feng Ying Wang
Abstract: In this paper, we make use of the integral method which is commonly used in partial differential equations to get the difference scheme on five points, and then construct an anisotropic diffusion model based on the partial differential equation. The numerical experimental results show the diffusion model can effectively magnify the image, and can keep the edge character and details of the image. It is proved that the numerical computational method proposed for solving the model is very effective.
Authors: Song Bai Cai, Da Zhi Li, Chang Wan Kim, Pu Sheng Shen
Abstract: The conventional solution strategy for nonlinear FEM of structural analysis is usually based on Newton-Raphson iteration under an additional constraint equation. So far a lot of nonlinear finite element solution procedures have been devised to provide the basis for most nonlinear finite element computer programs. In order to produce effective, robust solution algorithms, additional constraint equations for nonlinear FEM calculations in the load-displacement space of has been extensively investigated for the last a few decades. However, it is widely believed that due to the additional computations in the controlling of steps and directions of the iteration procedure, there will be more round-off errors accumulated to influence the convergence of solution. In this work, a more simplified solution procedure is presented, which is featured to be with neither iterations nor constraints. A Fortran computer program of the algorithm presented has been implemented in combining with a space truss element of co-rotational procedure. Verification of the procedure has been done by numerical example and a good result achieved.
Authors: Kai Yu Hao, Vadim Miroshnikov
Abstract: The numerical method of calculation of electromagnetic field in a control sample at a time of work of encircling eddy current transducer is offered. The method is based on a numerical solution of the two Maxwell equations, which connect a change of electrical and magnetic fields. It allows to make calculations taking into account the actual value of magnetic inductivity of metal and to get results in any form, convenient for further interpretations. For the calculation of the encircling eddy current transducer the equivalent circuit of defect as step junction is offered. The numerical calculation shows, that the greatest sensitivity of the transducer is achieved when the value of magnetic permeability of the object of control is approximately 10-30. Therefore, it is not necessary to lead the material of the object of control up to satiety, as it considered before.
Authors: Hong Sheng, Fang Ju Li, Yong Qin Liu
Abstract: The relationship between the length of the objects reflections on the water surface and the following factors including the spacing of objects and people,height of objects,observers’ height and the size of wave are discussed. According to the law of light reflection, a parametric equation is established among them. Secondly, the numerical solutions of the equation can obtained by MATLAB and draw the virtual image of the material point in the water. Besides, the objects reflection on the water surface with slight wave was simulated. Finally, a detailed qualitatively analysis for the relevant factors which affect the length of reflection are made and explains the physical phenomenon successfully.
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