The current thesis studies the modelling of turbulent reacting flows over a wide range of
combustion regimes and fuels and, in particular, the impact of molecular fluxes. The flow
is described using Favre Averaged Navier Stokes (FANS) equations with the scalar field
modelled using a transported joint-scalar probability density function (pdf) method solved
using a Monte Carlo approach with the method of fractional steps. The main focus of
this work is the understanding of the interactions between fluid flow and chemistry across
the scales in an internal combustion engine (ICE) with the aim to enable the prediction of
chemical species concentrations adjacent to solid surfaces. For the study of the heat and
mass transport across the various boundary layers, an explicit deterministic approach of
the molecular transport term is applied without assumptions. Hence, the current approach
conforms with the laminar flow limit in the absence of turbulence. Initially, the parallelisation
of the independent stochastic particles as an enabling tool was implemented based on
their thermochemical properties. The modelling of the laminar fluxes was introduced in a
consistent way to enable the modelling of the heat and mass transfer across all boundary layers
from the gas phase to the solid surface. Application of the laminar fluxes implementation
was initially presented for auto-ignition in a jet flame, a configuration related to compression
ignition engines and a detailed comparison of the influence of laminar and turbulent transport
on the evolution of the species concentrations is shown. Subsequently, the laminar fluxes were
applied for a range of freely propagating turbulent premixed flames, a configuration related
to spark ignition engines. A range of fuels was considered from hydrogen to iso-octane,
including practical conditions, and results show improved agreement with experimental data.