A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows
Journal of Computational Physics
A further study of numerical errors in large-eddy simulations
Journal of Computational Physics
A quadrature-based moment method for dilute fluid-particle flows
Journal of Computational Physics
A quadrature-based third-order moment method for dilute gas-particle flows
Journal of Computational Physics
Higher-order quadrature-based moment methods for kinetic equations
Journal of Computational Physics
Realizable high-order finite-volume schemes for quadrature-based moment methods
Journal of Computational Physics
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The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.