An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-28 DOI:10.1007/s00021-024-00851-w

Pengshan Wang, Wei Liu, Gexian Fan, Yingxue Song

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Abstract

In this paper, the Marker and Cell scheme based on a two-grid algorithm is proposed for the two-dimensional incompressible Darcy–Brinkman–Forchheimer equations in porous media. The motivation of the two-grid Marker and Cell algorithm is figuring out a nonlinear equation on a coarse grid with mesh size H and a linear equation on a fine grid with mesh size h. A small positive parameter \(\varepsilon \) is introduced. By using it, the non-differentiable nonlinear term can be transformed into the term which is twice continuously differentiable. The error estimates of the velocity and pressure in the \(L^2\) norms are obtained, which show \(O(\varepsilon +H^4+h^2)\). Second-order accuracy for some terms of velocity in the \(H^1\) norms is also obtained. Several numerical experiments are provided to confirm the availability of this efficient second-order algorithm. Behavior of the fluid flow with different Brinkman number is considered.

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非线性不可压缩达西-布林克曼-福克海默模型的高效二阶算法和 MAC 方案

本文针对多孔介质中的二维不可压缩达西-布林克曼-福克海默方程，提出了基于双网格算法的 Marker and Cell 方案。双网格 Marker and Cell 算法的动机是在网格尺寸为 H 的粗网格上计算非线性方程，在网格尺寸为 h 的细网格上计算线性方程。通过使用它，不可微的非线性项可以转化为两次连续可微项。得到了速度和压力在 \(L^2\) 规范下的误差估计，显示了 \(O(\varepsilon +H^4+h^2)\).在 \(H^1\) 规范下，一些速度项的二阶精度也得到了。提供了几个数值实验来证实这种高效二阶算法的可用性。考虑了不同布林克曼数的流体流动行为。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.