Assessment of Numerical Accuracyof PDF/Monte Carlo Methodsfor Turbulent Reacting Flows

This study is to explore the numerical features of a particle-mesh algorithm developed for a stand-alone joint velocity-frequency-composition PDF method for turbulent reactive flows. Numerical experiments are performed on a piloted-jet nonpremixed turbulent flame of methane to characterize and quantify various numerical errors in terms of numerical parameters: number of particles per cell Npc, number of cells M2, and time step 1t . First, a stationary solution is obtained and is verified to be independent of the time step 1t . Then, the total numerical error is identified as statistical error, bias, and discretization error. It is revealed that the statistical error converges as N−1/2 pc , and the bias as N−1 pc . The statistical error can be reduced by time-averaging or by performing multiple independent simulation (e.g., with a parallelized program). Finally, the scheme is shown to be second-order accurate— the spatial discretization error converging as M−2. A modified turbulence frequency model based on the turbulence production-to-dissipation ratio is shown to improve the numerical behavior of the turbulence model. These results demonstrate that the particle-mesh method is convergent. Also, the optimal numerical parameters, minimizing computational cost subject to a specified error tolerance, are estimated. An error reduction scheme, similar to Richardson extrapolation, is proposed and shown to be quite effective in reducing the deterministic error. c © 1999 Academic Press