ALADINS: an ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations. We address a time-adaptive solver specifically devised for the incompressible Navier-Stokes (INS) equations. One of the challenging issues in this context is the identification of a reliable a posteriori error estimator. Typical strategies are based on the combination of the solutions computed either with two different time steps or two schemes with different accuracy. In this paper, we move from the pressure correction algebraic factorizations formerly proposed by F. Saleri and A. Veneziani [SIAM J. Numer. Anal. 43, No. 1, 174–194 (2005; Zbl 1128.76047)]. These schemes feature an intrinsic hierarchical nature, such that an accurate solution for the pressure is obtained by computing intermediate low-order guesses. The difference between the two estimates provide a natural a posteriori estimator. After introducing the incremental formulation of the pressure correction schemes, we address the properties of this approach, including extensive implementation details. Numerical results presented refer to 2D and 3D unstructured problems, with a particular emphasis on cardiovascular problems, which are expected to largely benefit from time-adaptive solvers. In memory of F. Saleri (1965–2007).

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