A Two-grid Finite Element / Reduced Basis method for fluid dynamics problems
Résumé
For the real-time or many-query context classical discretization techniques such as finite element methods are generally too expensive. The reduced basis method exploits the parametric structure of the governing PDEs to construct rapidly, convergent and computationally efficient approximations. steady Navier-Stokes equations which requires treatment of non-linearities and non-affine parametric dependence. In an industrial framework, for optimization processes for instance these reduced basis methods have a great potential. One of the keys of this technique is the decomposition of the computational work into an off-line and on-line stage. However in some situation, it’s not possible to perform all the off-line computations required with an efficient performance of the reduced method. For example when the simulation code is used as a black box, one won’t be able to perform a very fast and cheap online stage. For this reason, we proposed an alternative method. The aim of this work is to provide tests to validate and generalize our method to fluid dynamics problems.
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