Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2024-01-10 DOI:10.3390/computation12010011

İ. Bağlan, Erman Aslan

引用次数: 0

Abstract

A two-dimensional heat diffusion problem with a heat source that is a quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are employed. As the problem is nonlinear, Picard’s successive approximation theorem is utilized. We demonstrate the existence, uniqueness, and constant dependence of the solution on the data using the generalized Fourier method under specific conditions of natural regularity and consistency imposed on the input data. For the numerical solution, an implicit finite difference scheme is used. The results obtained from the analytical and numerical solutions closely match each other.

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带周期性边界条件的二维传热的分析和数值研究

对一个二维热扩散问题进行了分析和数值研究，该问题带有一个热源，属于准线性抛物线问题。采用了周期性边界条件。由于问题是非线性的，因此采用了 Picard 逐次逼近定理。我们利用广义傅里叶方法，在输入数据的自然正则性和一致性的特定条件下，证明了解的存在性、唯一性和对数据的恒定依赖性。数值求解采用了隐式有限差分方案。分析和数值求解得出的结果非常吻合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.