Chapter 10 - Numerical approximations formulated as LES models

Abstract

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 can be based on effectively codesigned physics and numerical models solving the compressible conservation equations with nonoscillatory finite-volume algorithms. We evaluate three distinct numerical strategies for ILES and assess their impact simulating onset, development, and decay of turbulence: (i) the Harten–Lax–van Leer Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep – denoted split; (ii) the Harten–Lax–van Leer–Contact Riemann solver using a directionally unsplit strategy and parabolic reconstruction – denoted unsplit; (iii) the unsplit with a Low-Ma Correction – denoted unsplit*, addressing excessive numerical dissipation ∼1/Ma associated with upwinding in mixing applications driven by weakly-compressible local dynamics. Modified equation analysis, a technique for generating approximate equations for the computed solutions, is used to elucidate the effective subgrid models associated with the algorithms underlying ILES. Case studies considered are the Taylor–Green Vortex prototyping transition to turbulence, and Rayleigh–Taylor driven flow prototyping turbulent material mixing development. For given spatiotemporal resolution, significantly more accurate predictions (reduced numerical uncertainties) are provided by the unsplit discretizations, specially when augmented with the Low-Ma Correction. Relevant comparisons of ILES based on Euler and Navier–Stokes equations are presented. Overall, the unsplit* scheme reveals instrumental in capturing the spatiotemporal development of the Taylor–Green Vortex and Rayleigh–Taylor flows and their validation at prescribed Re on coarser grids.