Adaptive time-step with anisotropic meshing for incompressible flows

This paper presents a method of combining anisotropic mesh adaptation and adaptive time-stepping for Computational Fluid Dynamics (CFD). First, we recall important features of the anisotropic meshing approach using a posteriori estimates relying on the length distribution tensor approach and the associated edge based error analysis. Then we extend the proposed technique to contain adaptive time advancing based on a newly developed time error estimator. The objective of this paper is to show that the combination of time and space anisotropic adaptations with highly stretched elements can be used to compute high Reynolds number flows within reasonable computational and storage costs. In particular, it will be shown that boundary layers, flow detachments and all vortices are well captured automatically by the mesh. The time-step is controlled by the interpolation error and preserves the accuracy of the mesh adapted solution. A Variational MultiScale (VMS) method is employed for the discretization of the Navier–Stokes equations. Numerical solutions of some benchmark problems demonstrate the applicability of the proposed space–time error estimator. An important feature of the proposed method is its conceptual and computational simplicity as it only requires from the user a number of nodes according to which the mesh and the time-steps are automatically adapted.