TY - EJOUR
DO - 10.1016/j.jcp.2009.03.008
AB - This 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.
T1 - Reduced basis method for multi-parameter dependent steady Navier-Stokes equations: applications to natural convection in a cavity
IS - 12
DA - 2009
AU - Deparis, Simone
AU - Rozza, Gianluigi
JF - Journal of Computational Physics
SP - 4359-4378
VL - 228
EP - 4359-4378
N1 - EPFL-IACS report 12.2008
ID - 128722
KW - Reduced basis method
KW - a posteriori error estimation
KW - Brezzi-Rappaz-Raviart theory
KW - inf-sup constant
KW - steady incompressible Navier-Stokes equations
KW - natural convection
KW - Prandtl number
KW - Grashof number
UR - http://infoscience.epfl.ch/record/128722/files/Deparis_Rozza_JCP.pdf
ER -