Towards a Compressible Reactive Multiscale Approach Based on One-Dimensional Turbulence

Due to its huge complexity, progress in understanding and prediction of turbulent combustion is extremely challenging. In principle, progress is possible without improved understanding through direct numerical solution (DNS) of the exact governing equations, but the wide range of spatial and temporal scales often renders it unaffordable, so coarse-grained 3D numerical simulations with subgrid parameterization of the unresolved scales are often used. This is especially problematic for multi-physics regimes such as reacting flows because much of the complexity is thus relegated to the unresolved small scales. One-Dimensional Turbulence (ODT) is an alternative stochastic model for turbulent flow simulation. It operates on a 1D spatial domain via time advancing individual flow realizations rather than ensemble-averaged quantities. The lack of spatial and temporal filtering on this 1D domain enables a physically sound multiscale treatment which is especially useful for combustion applications where, e.g., sharp interfaces or small chemical time scales have to be resolved. Lignell et al. recently introduced an efficient ODT implementation using an adaptive mesh. As all existing ODT versions it operates in the incompressible regime and thus cannot handle compressibility effects and their interactions with turbulence and chemistry which complicate the physical picture even further. In this paper we make a first step toward an extension of the ODT methodology towards an efficient compressible implementation. The necessary algorithmic changes are highlighted and preliminary results for a standard non-reactive shock tube problem as well as for a turbulent reactive case illustrate the potential of the extended approach.