Combined PDF/SPH method for compressible turbulent flows.

摘要

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 which combines techniques borrowed from the field of smoothed particle hydrodynamics (SPH). This combination gives the method a unique ability to extract mean quantities, including the mean pressure gradient, directly from the particles using a grid-free approach. Two algorithms which greatly reduce the computational work for SPH in 1D and 2D have been developed to implement the method; for a simulation with N particles the computational work scales purely as {dollar}{lcub}cal O{rcub}(N).{dollar} The particle method has also been combined with a variance-reduction technique which can significantly reduce statistical error in first and second moments of selected mean flow quantities. When used with a second-order accurate predictor/corrector scheme, the resulting particle method provides a feasible way to obtain accurate PDF solutions to compressible turbulent flow problems. Results are presented for a variety of quasi-1D and 2D flows to demonstrate the method's robustness. These include solutions to both statistically stationary and nonstationary problems, and use both periodic and characteristic-based inflow/outflow boundary conditions. A 2D plane wake simulation also includes comparisons with experimental data and shows good agreement in spite of the simple turbulence model used. Comprehensive studies of numerical errors have also been performed, including a convergence study of the method. Detailed results are presented which confirm the expected behavior of each error.