Stochastic fields with adaptive mesh refinement for high-speed turbulent combustion

This paper presents a fully compressible joint velocity-species-energy probability density function (PDF) for modelling turbulent reactive flows across all Mach numbers. By incorporating velocities into the PDF, the approach unifies the treatment of non-linear source and turbulent transport terms with minimal model parameters. The PDF transport is solved using Eulerian stochastic fields, leveraging features from existing grid-based solvers like high-order shock-capturing schemes and adaptive mesh refinement. Validation test cases show that the solver achieves the theoretical convergence rate, maintains accuracy across refinement levels, and demonstrates convergence with a moderate number of fields. Additionally, it outperforms the Smagorinsky model by adding dissipation only when necessary. When applied to a supersonic jet flame, the solver reproduces experimental measurements and results from highly-resolved large eddy simulations, demonstrating robustness in supersonic reacting flows with dynamic flow fields and shocklet structures.