Numerical solution of parametrized Navier-Stokes equations by reduced basis methods

We apply the reduced basis method to solve Navier-Stokes equations in parametrized domains. Special attention is devoted to the treatment of the parametrized non-linear transport term in the reduced basis framework, including the case of non-affine parametric dependence that is treated by an empirical interpolation method. This method features (i) a rapid global convergence owing to the property of the Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in the parameter space, and (ii) the offline/on-line computational procedures which decouple the generation and projection stages of the approximation process. This method is well suited for the repeated and rapid evaluations required ∗currently at MIT, Mech.Eng.Dpt., room 3-264, 77 Mass Avenue, 02142 Cambridge MA (USA), [email protected].