Comparative analysis of nondimensionalization approaches for solving the 2-D differentially heated cavity problem

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-03-30 DOI:10.1002/fld.5285

F. I. Molina-Herrera, L. I. Quemada-Villagómez, J. L. Navarrete-Bolaños, H. Jiménez-Islas

引用次数: 0

Abstract

This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2-D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 10³ and 10⁸, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.

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解决二维不同加热腔问题的非尺寸化方法比较分析

本研究报告对解决二维差分加热空腔经典问题常用的三种非尺寸化方法的效果进行了数值研究。使用 Legendre 多项式正交配位法对控制方程进行离散化，并通过牛顿-拉斐尔森法和 LU 因式分解法求解所得到的代数系统。在考虑普朗特数等于 0.71 和几何长宽比等于 1 的情况下，对 103 到 108 之间的瑞利数进行了模拟，分析了流线、等温线和努塞尔特数的收敛性和计算时间。能提供独立结果的网格尺寸为 51 × 51。方法 II 最适合于差热空腔问题的非尺寸化。

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来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.