Numerical simulation on staggered grids of three-dimensional brinkman-forchheimer flow and heat transfer in porous media

IF 2.1 3区地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computational Geosciences Pub Date : 2024-01-05 DOI:10.1007/s10596-023-10266-7

Wei Liu, Yingxue Song, Yanping Chen, Gexian Fan, Pengshan Wang, Kai Li

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Abstract

In this paper, three-dimensional numerical algorithm is constructed to simulate the behavior of the Brinkman-Forchheimer flow and thermal fields. Numerical results of velocity, pressure and temperature are obtained by applying the efficient modified two-grid marker and cell (MAC) algorithm on staggered grids with the second-order backward difference formula (BDF2) time approximation. The modified-upwind idea is introduced to convective heat transfer equations for improving accuracy without any numerical oscillation. The second-order convergence rate can be achieved for pressure, velocity and temperature of considered three-dimensional model. Some numerical experiments are presented to illustrate the efficiency of algorithm. The numerical example with analytical solution is used to validate the effectiveness and accuracy of the algorithm by comparing with the results of traditional MAC algorithm. A time-dependent test is proposed to show a detailed sensitivity analysis to indicate the influence of parameters including the \(\varepsilon \), Forchheimer number, Brinkman number and thermal diffusivity on the physical properties of Brinkman-Forchheimer flow and heat transfer in porous media.

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在交错网格上对多孔介质中的三维布林克曼-福克海默流动和传热进行数值模拟

本文构建了三维数值算法来模拟布林克曼-福克海默流和热场的行为。通过在交错网格上应用二阶后向差分公式（BDF2）时间近似的高效修正双网格标记和单元（MAC）算法，获得了速度、压力和温度的数值结果。在对流传热方程中引入了修正上风思想，以提高精度，而不会产生任何数值振荡。所考虑的三维模型的压力、速度和温度都能达到二阶收敛率。一些数值实验说明了算法的效率。通过与传统 MAC 算法的结果进行比较，使用带有分析解的数值示例来验证算法的有效性和准确性。提出了一个随时间变化的测试，以显示详细的敏感性分析，说明包括（\varepsilon \）、福克海默数、布林克曼数和热扩散率在内的参数对多孔介质中布林克曼-福克海默流动和传热的物理特性的影响。

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来源期刊

Computational Geosciences 地学-地球科学综合

CiteScore

6.10

自引率

4.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Computational Geosciences publishes high quality papers on mathematical modeling, simulation, numerical analysis, and other computational aspects of the geosciences. In particular the journal is focused on advanced numerical methods for the simulation of subsurface flow and transport, and associated aspects such as discretization, gridding, upscaling, optimization, data assimilation, uncertainty assessment, and high performance parallel and grid computing. Papers treating similar topics but with applications to other fields in the geosciences, such as geomechanics, geophysics, oceanography, or meteorology, will also be considered. The journal provides a platform for interaction and multidisciplinary collaboration among diverse scientific groups, from both academia and industry, which share an interest in developing mathematical models and efficient algorithms for solving them, such as mathematicians, engineers, chemists, physicists, and geoscientists.