Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries (Communications in Computational Physics, 2011)
In this paper we consider (hierarchical, Lagrange) reduced basis approximationand a posteriori error estimation for potential flows in affinely parametrizedgeometries. We review the essential ingredients: i) a Galerkin projection onto a low-dimensionalspace associated with a smooth "parametric manifold" in order to get adimension reduction; ii) an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence;iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linear-functionaloutputs of interest and over the potential solution or related quantities ofinterest like velocity and/or pressure; iv) an Offline-Online computational decompositionstrategies to achieve a minimum marginal computational cost for high performancein the real-time and many-query (e.g., design and optimization) contexts. We presentthree illustrative results for inviscid potential flows in parametrized geometries representinga Venturi channel, a circular bend and an added mass problem.