Two-Dimensional PDF/SPH Simulations of Compressible Turbulent Flows

This paper describes recent progress made in the development and implementation of a two-dimensional Monte Carlo/PDF/SPH particle method. The approach, which is applicable to compressible turbulent flows, incorporates elements of smoothed particle hydrodynamics to extract mean quantities from the particles, including the mean pressure gradient. A new and efficient algorithm based on Fourier-series expansions of the SPH kernel is used to compute these means; for a simulation withNparticles the computational work scales purely asO(N). A thorough study of numerical errors introduced by the finite series expansion is also performed, and results are presented which show that these errors scale as expected and can be made negligibly small using modest computing requirements. The particle method has been used to simulate a variety of 2D flows, including a stationary turbulent plane wake, flows under the influence of simple body forces, and an unsteady flow featuring compression/expansion waves and a pair of decaying vortices. The plane wake calculation includes comparisons with self-similar experimental data and good agreement is obtained for the mean velocity and Reynolds stress profiles.