Finite element modified method of characteristics for the Navier-Stokes equations
2000; Wiley; Volume: 32; Issue: 4 Linguagem: Inglês
10.1002/(sici)1097-0363(20000229)32
ISSN1097-0363
AutoresAlejandro Allievi, Rodolfo Bermejo,
Tópico(s)Fluid Dynamics and Turbulent Flows
ResumoInternational Journal for Numerical Methods in FluidsVolume 32, Issue 4 p. 439-463 Research ArticleFull Access Finite element modified method of characteristics for the Navier–Stokes equations Alejandro Allievi, Corresponding Author Alejandro Allievi [email protected] Institute for Marine Dynamics, National Research Council of Canada, PO Box 12093, Station A, St. John's, Newfoundland, Canada A1B 3T5Institute for Marine Dynamics, National Research Council of Canada, PO Box 12093, Station A, St John's, Newfoundland, Canada A1B 3T5===Search for more papers by this authorRodolfo Bermejo, Rodolfo Bermejo Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid 28040, SpainSearch for more papers by this author Alejandro Allievi, Corresponding Author Alejandro Allievi [email protected] Institute for Marine Dynamics, National Research Council of Canada, PO Box 12093, Station A, St. John's, Newfoundland, Canada A1B 3T5Institute for Marine Dynamics, National Research Council of Canada, PO Box 12093, Station A, St John's, Newfoundland, Canada A1B 3T5===Search for more papers by this authorRodolfo Bermejo, Rodolfo Bermejo Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid 28040, SpainSearch for more papers by this author First published: 09 February 2000 https://doi.org/10.1002/(SICI)1097-0363(20000229)32:4 3.0.CO;2-YCitations: 54AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection–diffusion, Burgers and unsteady incompressible Navier–Stokes equations for laminar flow. Solutions for these progressively more involved problems are presented so as to give numerical evidence for the robustness, good error characteristics and accuracy of our method. To solve the Navier–Stokes equations, an approach that can be conceived as a fractional step method is used. The innovative first stage of our method is a backward search and interpolation at the foot of the characteristics, which we identify as the convective step. In this particular work, this step is followed by a conjugate gradient solution of the remaining Stokes problem. Numerical results are presented for: a Convection–diffusion equation. Gaussian hill in a uniform rotating field. b Burgers equations with viscosity. c Navier–Stokes solution of lid-driven cavity flow at relatively high Reynolds numbers. d Navier–Stokes solution of flow around a circular cylinder at Re=100. Copyright © 2000 John Wiley & Sons, Ltd. References 1J.P. Benqué, B. Iblier, A. Keramsi and G. Labadie, ' A finite element method for Navier–Stokes equations coupled with a temperature equation', in Fourth International Symposium on Finite Elements in Flow Problems, North-Holland, Amsterdam, 1982, pp. 295–301. 2J. Douglas and T.F. Russell, 'Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures', SIAM J. Numer. Anal., 19, 871–885 (1982). 3O. Pironneau, 'On the transport-diffusion algorithm and its applications to the Navier–Stokes equations', Numer. Math., 38, 309–322 (1982). 4A. Allievi and R. 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