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This paper presents a detailed characterization of the local and global errors associated with the in situ adaptive tabulation (ISAT) algorithm, which is used in conjunction with a transported PDF method. Calculations of a non-premixed turbulent methane/air piloted jet flame (Sandia flame D) using a skeletal chemical mechanism were performed using ISAT coupled with the computational fluid dynamics (CFD) code FLUENT. The three strategies implemented in ISAT for the growing of the ellipsoids of accuracy (EOAs) are discussed, and the cumulative distribution function (CDF) of the local error is presented for each of the three growing strategies. Computations are also performed to characterize the global error in the ISAT/PDF calculation. The computations used to characterize the global error were performed in parallel to achieve substantial savings in computational time.
In general the local error is well controlled, but there is a small probability of relatively large errors. Results from the investigation suggest that large retrieve errors are due to the region of accuracy (ROA) being non-convex, where the ROA is the connected region for which the error does not exceed the error tolerance, ϵtol. The global error in ISAT is found to be small compared to statistical error for ϵtol ≤ 10−4, and is found to vary linearly with ϵtol.
Acknowledgements
The authors wish to thank S. A. Lantz and L. P. Chew for assistance in various parts of this work. This work is supported by the US Department of Energy grant number DE-FG02-90ER14128. This research was conducted using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, federal agencies, foundations, and corporate partners.
