Assessment of Numerical Accuracy of PDF/Monte Carlo Methods for Turbulent Reacting Flows

Abstract

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 cellNpc, number of cells M2, and time step Δ t. First, a stationary solution is obtained and is verified to be independent of the time step Δ t. Then, the total numerical error is identified as statistical error, bias, and discretization error. It is revealed that the statistical error converges as Npc−1/2, and the bias as Npc−1. 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.