A Hybrid Algorithm for the Joint PDF Equation of Turbulent Reactive Flows

Abstract

In this paper a new particle-finite-volume hybrid algorithm for the joint velocity-frequency-composition PDF method for turbulent reactive flows is presented. This method is a combination of a finite-volume scheme and a particle method. The finite-volume scheme is used to solve the Reynolds averaged Navier–Stokes equations and the particle method to solve the joint PDF transport equation. The motivation is to reduce the bias and the statistical error and to have an algorithm which is more effi-cient than stand-alone particle-mesh methods. Therefore, in the particle method we use the smoother mean density h‰i and Favre averaged velocity ˜U fields computed by the finite-volume scheme: This scheme is an Euler solver for compressible flow with the turbulent fluxes and the reaction term, which are computed by the particle algorithm, as source terms. Since some of the quantities are computed twice (i.e., the mean density h‰i and the Favre averaged sensible internal energy ẽs), by the finite-volume scheme and by the particle method, the hybrid algorithm is redun-dant. Although the model differential equations are consistent, it was difficult to satisfy consistency numerically, and an accurate particle tracking algorithm is cru