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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 Formula: see text. 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.
Engelmann et al. (Tue,) studied this question.