PDF MODEL-CALCULATIONS OF COMPRESSIBLE TURBULENT FLOWS USING SMOOTHEDPARTICLE HYDRODYNAMICS

A particle method which applies the probability density function (PDF) method to compressible turbulent flows is presented. Solution of the PDF equation is achieved using a Lagrangian/Monte Carlo approach. A un ique feature of the method is its ability to calculate the mean pressu re gradient directly from the particles using a grid-free approach. Th is is accomplished by applying techniques borrowed from the field of s moothed particle hydrodynamics. Furthermore, these techniques have bee n implemented using a recently discovered algorithm which greatly redu ces the computational work in in. The particle method also incorporate s a variance-reduction technique which can significantly reduce statis tical error in first and second moments of selected mean flow quantiti es. When combined with a second-order accurate predictor/corrector sch eme, the resulting particle method provides a feasible way to obtain a ccurate PDF solutions to compressible turbulent flow problems. Results have been obtained for a variety of quasi-1D flows to demonstrate the method's robustness. These include solutions to both statistically st ationary and nonstationary problems, and use both periodic and charact eristic-based inflow/outflow boundary conditions. Convergence of the m ethod with respect to four different kinds of numerical errors has als o been studied. Detailed results are presented which confirm the expec ted convergence behavior of each error. (C) 1997 Academic Press.