Monte Carlo implementation of a single-scalar mapping closure for diffusion in the presence of chemical reaction

It is shown how to implement, via a Monte Carlo method, a single-scalar mapping closure for diffusion when chemical reactions or other processes are present. The mixing term in the one-point probability density function (pdf) equation of the scalar is closed via a mapping. The chemical term, closed in the pdf formulation, is treated exactly. To isolate each process, a fractional step technique is used. The methodology is the same if more processes are present. As an example, the pdf equation of one scalar reacting with itself in a statistically homogeneous forced turbulent flow is solved. Comparisons with computed direct numerical simulation data are excellent.