A realizable multivariate quadrature based approach for supersonic combustion modeling in LES

Filtered value of the combustion source term in large eddy simulation (LES) can be accurately estimated using the joint probability density function (PDF) of species mass fraction and enthalpy. Computing the PDF using traditional stochastic methods in shock-containing flows however leads to numerical instabilities. Recently an accurate quadrature based method called semi-discrete quadrature method of moments (SeQMOM) was developed by the authors for supersonic combustion modeling. The Eulerian and deterministic nature of this method ensures easy applicability in complex flows like supersonic combustors. Dispersion errors due to numerical implementation of quadrature based methods can however lead to non-realizable moments. In this work, we develop a realizable-SeQMOM methodology that ensures realizability of moments. Implementation of realizable-SeQMOM and validation with experiments is discussed.