Scalar conservation in large eddy simulations of reacting flows

Large eddy simulation is the most viable approach for the accurate simulation of turbulent reacting flows. With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. Furthermore, when higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. species mass fractions or progress variable). In this paper, we attempt to construct a numerical method that mitigates this issue.