A novel statistical method, termed the discrete probability function (DPF) method, for the calculation of probability density functions of scalar variables in a reacting flow is presented. The method relies on: (1) a solution of the transport equations for central values of bins in the discrete probability density functions (DPFS) of the coefficients and the boundary conditions, and (2) a calculation of the probability of the solutions using those of the coefficient and boundary value DPFS. An application of the method to a very simple, one dimensional reacting flow problem is presented and a comparison with the results of the conventional PDF transport equation method is made. The new method shows sufficient promise to justify future development for realistic turbulent reacting flow problems.
Gore, J.P., Sivathanu, Y.R., Discrete Probability Function (DPF) Method for Turbulent Reacting Flows, Combustion and Flame, Elsevier Science Pub, New York, NY, 1993.