Assessment of numerical accuracy of PDF Monte Carlo methods for turbulent reacting flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:152

Article

Xu, J ; Pope, SB

关键词: PDF Monte Carlo methods;    numerical convergence;    turbulent reactive flows;   

DOI  :  10.1006/jcph.1999.6241

来源: Elsevier

【 摘 要 】

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 non-premixed 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 Delta t. First, a stationary solution is obtained and is verified to be independent of the time step Delta 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-pc(-1/2), and the bias as N-pc(-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. (C) 1999 Academic Press.

【 授权许可】

Free