Impact of numerical hydrodynamics in turbulent mixing transition simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the HLL Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep -- denoted split; the HLLC solver using a directionally unsplit strategy and parabolic reconstruction -- denoted unsplit; and the HLLC solver using unsplit and a low-Ma correction (LMC) -- denoted unsplit*. Three case studies are considered: shock tube problems prototyping shock-driven turbulent mixing, the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and homogeneous isotropic turbulence.  Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC.  For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments – exhibiting higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.  Unsplit* schemes are also instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution.  -- Selected as Editor’s Pick, Phys. Fluids 33, 035126, 2021.