Revisiting the modelling of mixing time scales for Lagrangian filtered density function methods

Abstract

Mixing models for multiple mapping conditioning (MMC) methods are revisited as some details of their implementation have not yet been assessed. We use simulations of scalar mixing in non-reacting homogeneous isotropic decaying turbulence (HIT) such that (1) key modelling parameters can be taken from the direct numerical simulations without incurring additional modelling uncertainties and (2) direct validation is possible. Variants of Curl’s model are studied and direct comparison is sought with the variants’ performances in the context of standard (intensive) and sparse (such as MMC) particle approaches for the modelling of the probability density function (PDF). The second aim is to show the relative importance of micro-mixing and spatial diffusion in the presence of differential diffusion. The results demonstrate that MMC approximates the correct relaxation towards Gaussian independent of the mixing model’s variant. This is different from the standard PDF approach that requires a clear spatial localization given by the computational mesh to achieve a similar outcome. This spatial localization is not needed in MMC as the MMC mixing model already employs a localization in reference space. Differential diffusion effects can, however, only be accurately predicted if not only mixing but also spatial transport accounts for the differences in the molecular diffusion term. It is insufficient to adjust the mixing time scales only and future MMC models may require adjustments for accurate prediction capabilities.