A particle method applying the probability density function (PDF) appr
oach to turbulent compressible flows is presented. The method is appli
ed to several turbulent flows, including the compressible mixing layer
, and good agreement is obtained with experimental data. The PDF equat
ion is solved using a Lagrangian/Monte Carlo method. To accurately acc
ount for the effects of compressibility on the flow, the velocity PDF
formulation is extended to include thermodynamic variables such as the
pressure and the internal energy. The mean pressure, the determinatio
n of which has been the object of active research over the last few ye
ars, is obtained directly from the particle properties. It is therefor
e not necessary to link the PDF solver with a finite-volume type solve
r. The stochastic differential equations (SDE) which model the evoluti
on of particle properties are based on existing second-order closures
for compressible turbulence, limited in application to low turbulent M
ach number flows. Tests are conducted in decaying isotropic turbulence
to compare the performances of the PDF method with the Reynolds-stres
s closures from which it is derived, and in homogeneous shear flows, a
t which stage comparison with direct numerical simulation (DNS) data i
s conducted. The model is then applied to the plane compressible mixin
g layer, reproducing the well-known decrease in the spreading rate wit
h increasing compressibility. It must be emphasized that the goal of t
his paper is not as much to assess the performance of models of compre
ssibility effects, as it is to present an innovative and consistent PD
F formulation designed for turbulent inhomogeneous compressible flows,
with the aim of extending it further to deal with supersonic reacting
flows. (C) 1997 American Institute of Physics.