An a posteriori time error indicator for adaptive flow solvers

Abstract

This study introduces a novel a posteriori time error indicator applied to a finite element flow solver. The proposed approach integrates stabilized finite element techniques in space and backward differentiation formula (BDF) schemes in time, adjusting time step sizes dynamically in unsteady flow simulations. The developed time error indicator and time adaptivity algorithm encompass monolithic and fractional step algorithms. In the case of fractional step algorithms, an additional term is incorporated in the error indicator to account for the error caused by the splitting. A series of numerical examples are presented to validate the reliability and robustness of the time error indicator across benchmark problems involving incompressible and isentropic compressible flows.

J. Sekhavati gratefully acknowledges the support received from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 955923. R. Codina gratefully acknowledges the support received from the ICREA Acadèmia Program, from the Catalan Government. I. Martínez-Suárez gratefully acknowledges the support received from the Agència de Gestió d’Ajuts i de Recerca (AGAUR) through the predoctoral FI grant 2022-FI-B-00517.

Peer Reviewed

Postprint (published version)