TY - JOUR T1 - Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries JO - Communications in Computational Physics VL - 1 SP - 1 EP - 48 PY - 2011 DA - 2011/09 SN - 9 DO - http://doi.org/10.4208/cicp.100310.260710a UR - https://global-sci.org/intro/article_detail/cicp/7489.html KW - AB -

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error 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) an a posteriori error 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 minimum marginal computational cost for 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.