Quantitative analysis on implicit large eddy simulation

Abstract

Current research conducts the quantitative comparisons between implicit large eddy simulation (iLES) and explicit eddy-viscosity large eddy simulation (eLES). iLES and eLES in a compressible Taylor–Green vortex problem are implemented with a fourth-order finite-volume gas kinetic scheme. Compared with the key statistical quantities of direct numerical simulation, iLES outweighs eLES on the exactly same unresolved grids. With DNS solution, a priori analysis of compressible filtered subgrid-scale (SGS) turbulent kinetic energy ρ¯Ksgsf is performed. Forward and backward filtered SGS turbulent kinetic energy transfer coexists. The ensemble turbulent kinetic energy Ek is on the order of o(104) to o(102) of ensemble filtered SGS turbulent kinetic energy Ksgsf. The ensemble dominant physical dissipation rate ε1 is approximately 20 times larger than the ensemble filtered SGS dissipation rate −τijfS̃ijf. Then, for iLES and eLES, the total dissipation rate is decomposed into the resolved physical dissipation rate εphy, modeling SGS dissipation rate εsgsmod, and numerical SGS dissipation rate εsgsnum. Quantitative comparisons on the modeling SGS dissipation rate and numerical SGS dissipation rate in iLES and eLES are evaluated. The numerical dissipation in iLES can be treated as the built-in SGS dissipation, which accounts for the reasonable performance of iLES. While the explicit modeling SGS dissipation in eLES pollutes the resolved turbulent structures in such low-Reynolds number turbulence. The next generation of large eddy simulation on unresolved grids must take into account both the built-in numerical SGS dissipation and its competition explicit modeling SGS dissipation.