Theoretical and numerical analysis of a simple model derived from compressible turbulence

Sergey L. Gavrilyuk (1) , Jean-Marc Hérard (2, 3) , Olivier Hurisse (2) , Ali Toufaili (3, 2)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 EDF - EDF
3 I2M - Institut de Mathématiques de Marseille

Turbulent compressible flows are encountered in many industrial applications, for instance when dealing with combustion or aerodynamics. This paper is dedicated to the study of a simple turbulent model for compressible flows. It is based on the Euler system with an energy equation and turbulence is accounted for with the help of an algebraic closure that impacts the thermodynamical behavior. Thereby, no additional PDE is introduced in the Euler system. First, a detailed study of the model is proposed: hyperbolicity, structure of the waves, nature of the fields, existence and uniqueness of the Riemann problems. Then, numerical simulations are proposed on the basis of existing finite-volumes schemes. These simulations allow to perform verification test cases and more realistic explosion-like test cases with regards to the turbulence level.

Mots clés: Turbulence; compressible; hyperbolicity

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Sergey L. Gavrilyuk, Jean-Marc Hérard, Olivier Hurisse, Ali Toufaili. Theoretical and numerical analysis of a simple model derived from compressible turbulence. Journal of Mathematical Fluid Mechanics, 2022, ⟨10.1007/s00021-022-00676-5⟩. ⟨hal-03079453v2⟩