1999
DOI: 10.1006/jcph.1999.6241
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Assessment of Numerical Accuracy of PDF/Monte Carlo Methods for Turbulent Reacting Flows

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Cited by 99 publications
(107 citation statements)
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“…Note that, unlike many numerical methods, the time step in the present method is mainly restricted by the accuracy considerationsrather than the stability constraints and that the values of C u and C Ä are essentially chosen based on the work by Xu and Pope. 13 The conditional mean turbulent frequency Ä i; j is evaluated at the .i; j / grid point, and the velocity scales jU j and jV j are de ned as…”
Section: Analysis Of Local Time Steppingmentioning
confidence: 99%
“…Note that, unlike many numerical methods, the time step in the present method is mainly restricted by the accuracy considerationsrather than the stability constraints and that the values of C u and C Ä are essentially chosen based on the work by Xu and Pope. 13 The conditional mean turbulent frequency Ä i; j is evaluated at the .i; j / grid point, and the velocity scales jU j and jV j are de ned as…”
Section: Analysis Of Local Time Steppingmentioning
confidence: 99%
“…As remarked earlier, the bias is one of the dominant errors in the self-contained particle method [12,13]. Using the error decomposition in Eq.…”
Section: Biasmentioning
confidence: 99%
“…The main source of the bias is the statistical fluctuations in the particle fields used in the particle evolution equations. Both theoretical analysis and numerical experiments [30,13] have shown that the bias scales as N −1 pc . In Fig.…”
Section: Biasmentioning
confidence: 99%
“…The (deterministic) coefficients A(x, v) and B(x, v) are defined by the particular stochastic model, and there is much ongoing research as to both theoretically desirable [41,71,72,78] and practically desirable [86] forms for these coefficients. In chemically reacting or combusting systems, the equations (2) are augmented by another stochastic equation describing the local chemical composition at the particle's location [33,62,67].…”
Section: Introductionmentioning
confidence: 99%
“…The literature on developments and application of the purely Lagrangian simulation approach is proliferating, and in the introductory spirit of this paper, we confine ourselves to describing some foundational ideas in Section 4. We remark here that the Probability Density Function (PDF) and related Filtered Mass Density Function (FMDF) methodology developed by Pope and coworkers [64,67,68,80,86] and applied by several groups to problems in combustion [33,62] is a notable case of a purely Lagrangian simulation approach. We also would like to draw the reader's attention to the burgeoning field of Dissipative Particle Dynamics (DPD) [1,19,20,21,27,30,63], in which the small-scale dynamics of complex fluids, such as polymeric liquids, are simulated by a purely Lagrangian approach similar of similar character to those used in turbulence studies.…”
Section: Introductionmentioning
confidence: 99%