Publication Results



Code: 26/2012
Title: Model reduction based on Proper Generalized Decomposition for the Stochastic steady incompressible Navier-Stokes equations
Date: Monday 28th May 2012
Author(s) : Tamellini, L.; Le Maitre, O.; Nouy, A.
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Abstract: In this paper we consider a Proper Generalized Decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such technique is to compute a low-cost reduced basis approximation of the full Stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of pre-existing deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m deterministic problems for the construction of a m-dimensional reduced basis.