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A stabilized finite element method for transient Navier–Stokes equations based on two local Gauss integrations
Author(s) -
Jiang Yu,
Mei Liquan,
Wei Huiming
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2708
Subject(s) - finite element method , mathematics , discretization , mixed finite element method , gauss , temporal discretization , extended finite element method , mathematical analysis , hp fem , navier–stokes equations , reynolds number , rate of convergence , convergence (economics) , projection (relational algebra) , finite element limit analysis , physics , computer science , algorithm , turbulence , key (lock) , mechanics , computer security , compressibility , economics , economic growth , quantum mechanics , thermodynamics
SUMMARY On the basis of two local Gauss integrations, a stabilized finite element method for transient Navier–Stokes equations is presented, which is defined by the lowest equal‐order conforming finite element subspace (X h , M h) such asP 1− P 1(orQ 1 − Q 1 ) elements. The best algorithmic feature of our method is using two local Gauss integrations to replace projection operator. The diffusion term in these equations is discretized by using finite element method, and the temporal differentiation and advection terms are treated by characteristic schemes. Moreover, we present some numerical simulations to demonstrate the effectiveness, good stability, and accuracy properties of our method. Especially, the rate of convergence study tells us that the stability still keeps well when the Reynolds number is increasing. Copyright © 2011 John Wiley & Sons, Ltd.