Robust numerical schemes for Eulerian spray DNS and LES in two-phase turbulent flows

Large Eddy Simulation (LES) and Direct numerical Simulation (DNS) of polydisperse evaporating sprays with Eulerian models are promising tools for high performance computing of combustion applications. However, the spray system of conservation equations has a convective part which is similar either to general gas dynamics (GGD) Euler equations with a real gas type state law or to the pressureless gas dynamics (PGD), depending on the local flow regime and droplet Stokes number; henceforth, it usually features mathematical singularities due to model closure assumptions and requires dedicated numerical schemes. Here, we introduce a new generation of numerical methods based on relaxation schemes that are able to treat both PGD and GGD, as well as to cope in a robust manner with droplet vacuum zones and natural singularities of the resulting system of conservation equations. The proposed hybrid relaxation scheme and algorithms are validated through comparisons with analytical solutions and other numerical strategies in oneand two-dimensional configurations. They exhibit a robust behavior and are a promising candidate for more complex applications because they provide solutions to key numerical issues of the actual Eulerian spray DNS and LES models.