Direct and Implicit Large-Eddy Simulation of the Taylor-Green Vortex Flow

To demonstrate the potential advantages of highorder spatial and temporal numerical methods, direct numerical and implicit large-eddy simulation of the Taylor-Green vortex flow is computed using a variable-order finite-difference code on multi-block structured meshes. The spatial operators satisfy the summation-by-parts property, with block interfaces and boundary conditions enforced with simultaneousapproximation-terms. The solution is integrated in time with explicit-first-stage, singly-diagonallyimplicit Runge-Kutta methods. An investigation into artificial dissipation and spatial filtering shows filtering is much more computationally efficient at moderate Courrant numbers, however, it does eventually place a limit on the time step. Grid convergence studies show excellent performance of higher resolution simulations, accurately capturing the decay of kinetic energy with a decay proportional to t−2 after transition to turbulence. The simulations also produce very good energy spectra, approximating a k−5/3 law at peak dissipation. In contrast, the coarse resolution simulations do very poorly, overdissipating the solution early on. High-order simulations consistently better capture the location and height of the peak dissipation. Finally, temporal convergence studies demonstrate that high-order time integration has a superior level of efficiency, except for the coarsest temporal resolution simulations.