WS1 DNS of the Taylor-Green vortex at Re=1600

This problem is aimed at testing the accuracy and the performance of high-order methods on the direct numerical simulation of a three-dimensional periodic and transitional flow defined by a simple initial condition: the Taylor-Green vortex. The computational domain is a triply periodic cubic domain, in which initially 8 vortices reside, described by an analytical formula. This flow transitions to turbulence, with the creation of small scales, followed by a decay phase similar to decaying homogeneous turbulence.

Participants are expected to perform a grid independence study on Cartesian meshes, as well as a few computations on unstructured/perturbed meshes at similar resolution as the Cartesian ones. The assessment criteria consist of the evolution of the energy dissipation rate as well as the enstrophy. Further verification is done on the basis of the kinetic energy spectrum as well as the trace of the vorticity on the periodic plane at selected time steps.

Computations need to be run on Cartesian meshes with specified equivalent resolutions 64, 128 and 256. If applicable, it is expected that participants use the unstructured and perturbed meshes provided by the test case leader to guarantee a level playing field. These will be generated in function of the interpolation (order) used by the discretization.