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The joint probability density function (PDF) of thermochemical variables can be used for accurately computing the combustion source term. Quadrature based methods provide a computationally efficient and robust approach for estimating the PDF. The direct quadrature method of moments (DQMOM) is well suited for multivariate problems like combustion. Numerical implementation of DQMOM however leads to errors in estimating the PDF. In this work, a new quadrature based approach called semi-discrete quadrature method of moments (SeQMOM) that overcomes this problem is developed. A decoupling procedure allows extension of this method to multivariate problems. SeQMOM is then used for studying an experimental Mach 2.2 supersonic cavity based combustor.

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