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An extension to the classical FPV model is developed for transcriticalreal-fluid combustion simulations in the context of finite volume, fullycompressible, explicit solvers. A double-flux model is developed fortranscritical flows to eliminate the spurious pressure oscillations. A hybridscheme with entropy-stable flux correction is formulated to robustly representlarge density ratios. The thermodynamics for ideal-gas values is modeled by alinearized specific heat ratio model. Parameters needed for the cubic EoS arepre-tabulated for the evaluation of departure functions and a quadraticexpression is used to recover the attraction parameter. The novelty of theproposed approach lies in the ability to account for pressure and temperaturevariations from the baseline table. Cryogenic LOX/GH2 mixing and reacting casesare performed to demonstrate the capability of the proposed approach inmultidimensional simulations. The proposed combustion model and numericalschemes are directly applicable for LES simulations of real applications undertranscritical conditions.

Numerical framework for transcritical real-fluid reacting flow simulations using the flamelet progress variable approach