A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models

Abstract

This research work focuses on the so-called non-intrusive model coupling procedure which has been proposed and widely analyzed in structural mechanics during the last decade, and which constitutes a flexible and attractive engineering simulation tool for the analysis of localized phenomena with low implementation effort. In this context, we propose verification tools that enable to certify the quality of approximate solutions obtained from such a non-intrusive model coupling. They consist in computable a posteriori error estimator and indicators, constructed in order to quantitatively assess the overall error level and the various error sources, and which are dedicated to the practical control of the error on outputs of interest. An adaptive algorithm is then defined in order to effectively and automatically drive the coupling process, and optimally adjust the coupling parameters (location of the coupling interface, local mesh size, number of iterations) so that a given error tolerance is reached with minimal computing resources. Performance of the approach is shown on several numerical experiments involving various quantities of interest and adaptivity scenarios.