Impact of Numerical Hydrodynamics in Coarse Grained Simulations of Turbulent Material Mixing

Underresolved simulations are typically 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.    ILES modeling can be based on effectively codesigned physics and numerics solving the compressible conservation equations with non-oscillatory finite-volume algorithms. We evaluate distinct numerical strategies for ILES and assess their impact simulating onset, development, and decay of turbulence: i) the Harten-Lax-van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep; ii) the Harten-Lax-Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction; and iii) the said unsplit scheme with added Low-Ma Correction (LMC) – denoted unsplit*.    The LMC addresses the problem of excessive leading numerical dissipation ~1/Ma associated with upwinding critical in many applications of interest where most of the mixing actually occurs where the flow is weakly compressible.   Modified equation analysis, a technique for generating approximate equations for the computed solutions, is used to elucidate the subgrid models associated with the algorithms underlying ILES.    Fundamental case studies considered in this presentation include, homogeneous isotropic turbulence, the Taylor-Green Vortex, Rayleigh-Taylor flow, and shock-tube studies.  For given spatiotemporal grid resolution, significantly more accurate predictions (reduced numerical uncertainties) are provided by the unsplit discretizations, specially when augmented with the LMC. Relevant comparisons of ILES based on Euler and Navier-Stokes equations are presented. Overall, the unsplit* reveals instrumental in capturing the spatiotemporal development and their validation on coarser grids.