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.

这项工作解决了当应用于反应流的假设概率密度函数 (PDF) 方法时 beta 分布的缺点，例如小火焰进程变量方法。无论参数值如何，β 分布都包含守恒标量的整个样本空间，这可以证明违反了偏微分方程的强最大值原理。为了解决这个问题，引入了一类新的概率分布，并在几个守恒的标量混合问题上进行了测试。新发行版不违反强最大原则，并且与传输 PDF 和 DNS 解决方案相比，与 beta 发行版相比，在数量上更一致。检查了过滤器宽度和停留时间的影响，并概述了对多个混合部分的扩展。