Direct numerical simulation of an unsteady wall-bounded turbulent flow configuration for the assessment of large-eddy simulation models

Abstract

A new benchmark case for the evaluation of direct numerical simulation (DNS) and large-eddy simulation (LES) models and methods is presented in this study. The known Taylor–Green vortex is modified by replacing the periodic boundary conditions in one direction with a no-slip boundary. A passive scalar is added and transported from the wall into the fluid. The addition of walls allows for the study of transient-instationary flows in a simple geometry with clean boundary and initial conditions, which is a key requirement for the assessment of LES modeling strategies. The added scalar mimics heat transfer through the wall. The case features reasonable computational cost for highly-resolved LES and DNS calculations. Simulations of the wall-bounded Taylor–Green vortex are easy to setup and do not require additional modeling. The proposed modification of the case is compared to the default Taylor–Green vortex and the difference in flow-physics is discussed. A detailed convergence study with four meshes, each of them refined by a factor of 2, has been conducted. The results reveal that converged second-order statistics can be obtained up to a dimensionless time of $t/t_0=20$. Beyond that, due to the unsteady chaotic nature of the flow, some uncertainties remain. The results show that the case features challenging (near-wall) flow dynamics, which cannot be covered using the default Taylor–Green vortex and hence, justify the proposed case as a useful benchmark.