The main objectives were to establish and investigate discontinuous and con
tinuous random walk models appropriate for free-shear hows with regard to t
urbulent particle diffusion. The models were designed to capture the crossi
ng trajectories effect, the continuity effect, and the inertial-limit effec
t, all for the case of heavy particles whose densities are much greater tha
n that of the surrounding fluid. In addition, both techniques included an i
sotropic drift velocity to account for inhomogeneous turbulence The computa
tional efficiency of the continuous random walk models is improved by utili
zing local time stepping, which effectively filters out high-frequency velo
city fluctuations that do not have a significant influence on particle diff
usion. The predictive performances of these two random walk models were exa
mined through comparison with experimental data and idealized test conditio
ns. The results indicate that both models agree well with experimental data
for a nearly homogeneous turbulent make and an inhomogeneous turbulent axi
symmetric jet (although the continuous random walk model performs somewhat
better for the inhomogeneous flows). It was also found that the proposed d
rift velocity models are important to ensure continuity when simulating par
ticle diffusion with inhomogeneous turbulence