Saad Raza, Abdul Rauf, Jamilu Sabi'u, Abdullah Shah
{"title":"A numerical method for solution of incompressible Navier–Stokes equations in streamfunction-vorticity formulation","authors":"Saad Raza, Abdul Rauf, Jamilu Sabi'u, Abdullah Shah","doi":"10.1002/cmm4.1188","DOIUrl":null,"url":null,"abstract":"<p>In this work, we have proposed a numerical approach for solving the incompressible Navier–Stokes equations in the streamfunction-vorticity formulation. The numerical scheme is based on the diagonally implicit fractional-step <math>\n <mrow>\n <mi>θ</mi>\n <mo>−</mo>\n </mrow></math>(DIFST) method used for the time discretization and the conforming finite element method for the spatial discretization. The accuracy and efficiency of the scheme are validated by solving some benchmark problems. The numerical simulations are carried out using the DUNE-PDELab open-source software package. The comparison of DIFST scheme with different time discretization schemes is provided in terms of CPU time. Also, different solvers with preconditioners are investigated for solving the resulting algebraic system of equations numerically.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1188","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Methods","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cmm4.1188","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
In this work, we have proposed a numerical approach for solving the incompressible Navier–Stokes equations in the streamfunction-vorticity formulation. The numerical scheme is based on the diagonally implicit fractional-step (DIFST) method used for the time discretization and the conforming finite element method for the spatial discretization. The accuracy and efficiency of the scheme are validated by solving some benchmark problems. The numerical simulations are carried out using the DUNE-PDELab open-source software package. The comparison of DIFST scheme with different time discretization schemes is provided in terms of CPU time. Also, different solvers with preconditioners are investigated for solving the resulting algebraic system of equations numerically.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
