Numerical investigation of a new class of models of Darcy-scale flows with flow-dependent permeability

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2024-11-22 DOI:10.1016/j.jcp.2024.113604

Alexander A. Belozerov, Natalia B. Petrovskaya, Yulii D. Shikhmurzaev

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Abstract

The Darcy model for flows in porous media is hugely popular among researchers and practitioners yet there are many problems where the classical Darcy model is not efficient and accurate as it gives rise to manifestly nonphysical singularities. We aim to investigate numerically a new class of mathematical models that allow for handling nonphysical singularities while preserving the advantages of the classical Darcy model. The introduced dependence of the permeability of the porous matrix on the flow that passes through it makes it necessary to compute the flow field and the permeability field simultaneously, and we therefore develop a novel numerical method to compute the solution to a strongly nonlinear system of PDEs arising in the problem. Our approach allows one to take characteristics of the flow geometry into account in numerical solution and we demonstrate the predictive potential of the generalized Darcy model through numerical tests.

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对具有随流渗透性的达西尺度流动新型模型的数值研究

多孔介质中流动的达西模型深受研究人员和从业人员的欢迎，但在许多问题上，经典达西模型并不高效和准确，因为它会产生明显的非物理奇点。我们的目标是对一类新的数学模型进行数值研究，在保留经典达西模型优点的同时，处理非物理奇点。由于多孔基质的渗透率与流经基质的水流有关，因此有必要同时计算流场和渗透率场，因此我们开发了一种新的数值方法来计算问题中出现的强非线性 PDE 系统的解。我们的方法允许在数值求解中考虑流动几何形状的特征，并通过数值测试证明了广义达西模型的预测潜力。

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

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.