Wc. Welton et Sb. Pope, PDF MODEL-CALCULATIONS OF COMPRESSIBLE TURBULENT FLOWS USING SMOOTHEDPARTICLE HYDRODYNAMICS, Journal of computational physics, 134(1), 1997, pp. 150-168
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.