Robust numerical coupling of pressure and pressureless gas dynamics equations for Eulerian spray DNS and LES

Matthieu Boileau (1, 2) , Christophe Chalons (2, 3) , Marc Massot (1, 2)

1 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
2 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
3 LMV - Laboratoire de Mathématiques de Versailles

Large Eddy Simulation (LES) and Direct numerical Simulation (DNS) of polydisperse evaporating sprays with Eulerian models are very promising tools for high performance computing of combustion applications. They are able to describe the turbulent dispersion and evaporation and properly predict the combustion regimes. However, the spray system of conservation equations has a convective part which is either similar to gas dynamics 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; so, they usually involve singularities due to model closure assumptions and require dedicated numerical schemes. Besides, it is desirable to cope with exactly zero droplet density in some zones of the flow, especially near the injection zone, where droplets are injected in only some spatial locations. Though the issue has been successfully tackled in the framework of PGD with the use of accurate kinetic schemes, it cannot be directly extended to general gas dynamics. The purpose of the present contribution is to introduce a new generation of numerical methods based on relaxation schemes which are able to treat both PGD and general gas dynamics, as well as to cope in a robust manner with 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 on 1D and 2D configurations. They exhibit a very robust behavior and are a very promising candidate for more complex applications since they provide solutions to key numerical issues of the actual Eulerian spray DNS and LES models.

Mots clés: Large Eddy Simulation; Relaxation schemes; Spray equation; Multi-fluid models

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Matthieu Boileau, Christophe Chalons, Marc Massot. Robust numerical coupling of pressure and pressureless gas dynamics equations for Eulerian spray DNS and LES. SIAM Journal on Scientific Computing, 2014, pp.1-23. ⟨hal-00906220v1⟩