An efficient algorithm for scalar PDF modelling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micro-mixing models

In this paper, we investigate the application of probability density function (PDF) Monte Carlo methods to scalar release from small sources in a turbulent flow spanning a large physical domain. This is a typical situation encountered when modeling the dispersion of a gaseous substance in the atmosphere. Monte Carlo PDF methods have recently been applied to atmospheric modeling responding to the need for predicting the higher statistics and the concentration PDF generated by the continuous release of reactive and non-reactive substances. In this work we introduce some optimized numerical techniques based on the paradigm that the main field of interest is the scalar field and not the fluid dynamic field; the scalar are considered dynamically passive and the statistical characteristics of the turbulence velocity field are assumed known. These techniques are a block-structured grid coupled with a particle splitting/erasing algorithm and a localized time stepping. The proposed technique is different from others presented before since the particle splitting and erasing is done in a more straightforward and consistent manner. This method has been applied to the study of scalar dispersion from localized line sources in a canopy generated boundary layer. The line source has been treated as a point source in a two-dimensional space but the extension to three dimensions is straightforward. Our framework allows for an evaluation of the effects induced by different levels of discretization in the velocity space of the involved micro-mixing model, starting from the interaction by the exchange with the mean (IEM) toward the more physically consistent interaction by exchange with the conditional mean (IECM). Therefore, aside from the algorithm description and a complete numerical analysis of the code, a comparison between the IEM and IECM micro-mixing models has been investigated.