矩形管道电势数值计算与解析计算的结果比较

IF 4.6 Q1 OPTICS Journal of Physics-Photonics Pub Date : 2023-11-01 DOI:10.1088/1742-6596/2623/1/012036
Z S Maulana, M F R Rizaldi, M A Bustomi
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引用次数: 0

摘要

求解矩形管道内电位分布问题可采用两种方法:数值法和解析法。利用拉普拉斯方程和给定的边界条件得到解析解,以正弦函数和双曲函数的线性组合形式完成解。而在Python编程语言中使用有限差分法得到了数值解。解析解与数值解的比较表明,两者具有较好的拟合性。这可以从两种方法得到的矩形管内的电势分布图中看出。在Python编程语言中使用有限差分法得到的数值解,为求解矩形管道的电势分布问题提供了准确、高效的结果。利用解析法中的前四项,在管道上选取A点(3.33,1.67)、B点(3.33,3.34)、C点(6.67,1.67)、D点(6.67,3.34)4个观测点,得到解析法与数值法的电位值差值分别为35.91%、51.96%、51.96%、35.91%。如果在解析计算中采用更多的项,并且在管道上考虑更多的观测点,那么解析方法与数值方法的值差将会变小。
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The Results Comparison of Numerical and Analytical Methods for Electric Potential on Rectangular Pipes
Abstract Two methods can be used to solve the problem of electric potential distribution in a rectangular pipe: numerical and analytical. The analytical solution is obtained using the Laplace equation and the given boundary conditions to complete the solution in the form of a linear combination of sinusoidal and hyperbolic functions. While the numerical solution is obtained using the finite difference method in the Python programming language. The comparison between the analytical and numerical solutions shows that the two have a good fit. This can be seen from the graph of the electric potential distribution in the rectangular pipe produced by the two methods. Numerical solutions obtained using the finite difference method in the Python programming language provide accurate and efficient results in solving the problem of the electric potential distribution in rectangular pipes. The use of the first four terms in the analytical method and the selection of 4 observation points on the pipe, namely points A (3.33, 1.67), B (3.33, 3.34), C (6.67, 1.67), and D (6.67, 3.34) produces a difference in the electric potential value between analytical and numerical methods each point is 35.91%, 51.96%, 51.96%, and 35.91%. The value difference between analytical and numerical methods will be smaller if more terms are taken in the analytical calculation, and more observation points are considered on the pipe.
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来源期刊
CiteScore
10.70
自引率
0.00%
发文量
27
审稿时长
12 weeks
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