Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

Abstract

AbstractIn this paper we consider (hierarchical, Lagrange) reduced basis approximation anda posteriorierror estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence; iii) ana posteriorierror estimation procedure: rigorous and sharp bounds for the linear-functional outputs of interest and over the potential solution or related quantities of interest like velocity and / or pressure; iv) an Offline-Online computational decomposition strategies to achieve a minimummarginal computational costfor high performance in the real-time and many-query (e.g., design and optimization) contexts. We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel, a circular bend and an added mass problem.