ABSTRACT A novel, efficient method to account for multivariate probability density functions (PDFs) in the context of the flamelet generated manifolds (FGM) approach in a large eddy simulation (LES) framework is presented and discussed. It consists of applying the ‘Correlation Set by Simulated Annealing (CSSA)’ algorithm on univariate samples of each control variable to recombine them into multivariate samples in joint space, while accounting for the needed covariances. This is done on the fly and on a cell-by-cell basis. Thereby, the assumption of statistical independence of the control variables has been relaxed. The PDF is represented in a discrete manner and the integration is replaced through ensemble averaging. Consequently, the shape of the PDF no longer appears in the look-up table. The algorithm has been validated in the context of LES calculations of two configurations. Compared to a conventional pre-integrated FGM approach, the required CPU time has increased only modestly.

We present results of numerical modelling of dispersion of a passive pollutant over a middle-size city in complex hilly terrain under different initial thermal stratification conditions. The computations were performed in the time-dependent Reynolds-Averaged Navier-Stokes (T-RANS) framework, using an algebraic three-equation (AFM k – e –  ) turbulence model for subscale heat and concentration fluxes. Considered are two scenarios that mimic relevant meteorological conditions. The first is a typical windless winter day with distinct potential temperature inversions (at 800m and 300m above the valley ground with a gradient of 4 K/km in the upper atmosphere) where the transport of pollutants is solely driven by thermal buoyancy effects generated by heat islands. A multi-zonal approach was used to define different levels of heat and concentration emissions within the city. The second case was forced and mixed convection with neutral stratification for the city centre at a neighborhood scale with pre-defined approaching wind. Here, a non-uniform building-resolving mesh (down to 3.5m) was used with traffic emissions along all major roads as the primary pollution sources. The simulations provided details of spatial and temporal evolution of flow and scalar fields over the city.