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 N pc , number of cells M 2 , and time step t. First, a stationary solution is obtained and is verified to be independent of the time step t. 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 accuratethe 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.