Alternatives to the Beta Distribution in Assumed PDF Methods for Turbulent Reactive Flow

This work addresses a shortcoming of the beta distribution when applied to assumed probability density function (PDF) methods for reactive flow, such as the flamelet-progress variable method. Regardless of parameter values, the beta distribution contains the entire sample space of a conserved scalar, which can be shown to violate the strong maximum principle of partial differential equations. To remedy this, a new class of probability distributions is introduced and tested on several conserved scalar mixing problems. The new distributions do not violate the strong maximum principle, and are in better quantitative agreement with transported PDF and DNS solutions than the beta distribution. The effects of filter width and residence time are examined, and extensions to multiple mixture fractions are outlined.