{"title":"Pressure-correction projection method for modelling the incompressible fluid flow in porous media","authors":"K. Terekhov","doi":"10.1515/rnam-2023-0019","DOIUrl":null,"url":null,"abstract":"Abstract This work is dedicated to the pressure-correction projection method for the volume-averaged Navier–Stokes system for porous media. A set of parameters controlling the presence of inertia and viscosity is introduced into the system. Switching parameters allows us to reduce the system to either the Brinkman system or the Darcy equation. Considering the jump in the parameters between mesh cells allows capturing the contact of media of different types, such as free-flow and porous media flow. We apply Chorin’s projection method to decouple the system. The splitting of the system yields a momentum conservation equation and an anisotropic pressure correction equation. We propose a combination of collocated finite-volume methods to solve the problem.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"241 - 265"},"PeriodicalIF":0.5000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Numerical Analysis and Mathematical Modelling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/rnam-2023-0019","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This work is dedicated to the pressure-correction projection method for the volume-averaged Navier–Stokes system for porous media. A set of parameters controlling the presence of inertia and viscosity is introduced into the system. Switching parameters allows us to reduce the system to either the Brinkman system or the Darcy equation. Considering the jump in the parameters between mesh cells allows capturing the contact of media of different types, such as free-flow and porous media flow. We apply Chorin’s projection method to decouple the system. The splitting of the system yields a momentum conservation equation and an anisotropic pressure correction equation. We propose a combination of collocated finite-volume methods to solve the problem.
期刊介绍：
The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest.
Topics:
-numerical analysis-
numerical linear algebra-
finite element methods for PDEs-
iterative methods-
Monte-Carlo methods-
mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.
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