Short note: empirical findings for spatial and temporal discretization orders for the Taylor – Green vortex

Abstract

PurposeThe purpose of this paper is to shed some light into the equivalency of grid size and spatial and temporal orders of accuracy for turbulent flows.Design/methodology/approachThis paper compared several finite difference schemes on various meshes and various orders of accuracy for the canonical Taylor–Green vortex testcase.FindingsA remarkable empirical result observed is that the accuracy of eighth-order schemes on grids of size 2 h was equivalent to second-order schemes on grids of size h. This was the case when going from 1003 to 2003 as well as from 2003 to 4003. In all these cases, kinetic energy, vorticity and numerical dissipation were compared in detail.Research limitations/implicationsThe results obtained were carried out using finite difference solvers. It remains to be seen if similar behaviors are also observed for other numerical schemes.Originality/valueThese (surprising) findings should be of interest to the larger community.