An adaptive numerical method for solving EDQNM equations for the analysis of long-time decay of isotropic turbulence

Abstract

A new numerical formulation for the Eddy-Damped Quasi-Normal Markovian (EDQNM) model is proposed in the present paper. This formulation is based on an adaptive procedure that progressively modifies the spectral mesh at the large scales, forcing a resolution requirement set by the user.The resulting adaptive numerical method for the EDQNM model has been systematically tested by comparison with the classical model, covering a wide range of initial conditions. In particular, the sensitivity of the results to the initial Reynolds number Reλ and to the slope of the energy spectrum at the large scales σ (E(k→0)∝kσ) has been investigated. For all the initial conditions prescribed, the adaptive numerical method recovers exactly the same solution of the classical version. This result has been observed in the analysis of the main statistical quantities of interest, such as the turbulent kinetic energy K and the energy dissipation rate ε. The same conclusions have been drawn by the direct comparison of the energy spectra E.An extension of the adaptive numerical method for the analysis of sheared/rotating turbulence is as well proposed and successfully assessed.The numerical algorithm proves to be progressively more efficient when long-time simulations are performed. In particular, a reduction up to one order of magnitude in the computational resources required is observed. Due to its efficiency and precision, the adaptive formulation of the EDQNM model promises to be an optimal tool to be blended with the methods of the Uncertainty Quantification (UQ) theory, in order to provide new insights about isotropic turbulence decay.