Model reduction based on Proper Generalized Decomposition for the Stochastic steady incompressible Navier-Stokes equations

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.
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Lorenzo Tamellini, Olivier Le Maitre, Anthony Nouy. Model reduction based on Proper Generalized Decomposition for the Stochastic steady incompressible Navier-Stokes equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (3), pp.A1089-A1117. ⟨10.1137/120878999⟩. ⟨hal-00733733⟩

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