000128722 001__ 128722
000128722 005__ 20190117192124.0
000128722 0247_ $$2doi$$a10.1016/j.jcp.2009.03.008
000128722 02470 $$2ISI$$a000266506400006
000128722 037__ $$aARTICLE
000128722 245__ $$aReduced basis method for multi-parameter dependent steady Navier-Stokes equations: applications to natural convection in a cavity
000128722 269__ $$a2009
000128722 260__ $$c2009
000128722 336__ $$aJournal Articles
000128722 500__ $$aEPFL-IACS report 12.2008
000128722 520__ $$aThis work focuses on the approximation of parametric steady Navier-- Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute an output, and give sharp error bounds. The computations are split into an offline part, where the value of the parameters is not yet identified, but only within a range of interest, and an online part, where the problem is solved for an instance of the parameters. The offline part is expensive and is used to build a reduced basis and prepare all the ingredients -- mainly matrix-vector and scalar products, but also eigenvalue computations -- necessary for the online part, which is fast. We provide a model problem -- describing natural convection phenomena in a laterally heated cavity -- characterized by three parameters: Grashof and Prandtl numbers and the aspect ratio of the cavity. We show the feasibility and efficiency of the a posteriori error estimation by the natural norm approach considering several test cases by varying two different parameters. The gain in terms of CPU time with respect to a parallel finite element approximation is of three magnitude orders with an acceptable -- indeed less than 0.1% -- error on the selected outputs.
000128722 6531_ $$aReduced basis method
000128722 6531_ $$aa posteriori error estimation
000128722 6531_ $$aBrezzi-Rappaz-Raviart theory 
000128722 6531_ $$ainf-sup constant
000128722 6531_ $$asteady incompressible Navier-Stokes equations
000128722 6531_ $$anatural convection
000128722 6531_ $$aPrandtl number
000128722 6531_ $$aGrashof number
000128722 700__ $$0241667$$aDeparis, Simone$$g121157
000128722 700__ $$0240712$$aRozza, Gianluigi$$g149443
000128722 773__ $$j228$$k12$$q4359-4378$$tJournal of Computational Physics
000128722 8564_ $$zURL
000128722 8564_ $$s7033517$$uhttps://infoscience.epfl.ch/record/128722/files/Deparis_Rozza_JCP.pdf$$zn/a
000128722 909C0 $$0252102$$pCMCS$$xU10797
000128722 909CO $$ooai:infoscience.tind.io:128722$$pSB$$particle
000128722 937__ $$aCMCS-ARTICLE-2008-024
000128722 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000128722 980__ $$aARTICLE