A Lagrangian stochastic method of solving the diffusion equation for
inhomogeneous turbulence is presented in this paper. This numerical method uses (1) a first-order approximation for the spatial variation of the eddy diffusivity and (2) the corresponding first three particle position moments, to define a non-Gaussian particle position distribution. The method handles the case when the eddy diffusivity varies linearly to zero at a boundary. This is done by using the first few terms of the series
representation of the analytic solution for this case to construct the non-Gaussian position
distribution. Comparison of numerical simulation results to analytic solutions of the diffusion equation show that this method is accurate and significantly more efficient than
a previously used methods that assume a Gaussian particle position distribution.