An exact Riemann solver for multicomponent turbulent flow

Emmanuelle Declercq , Alain Forestier (1) , Jean-Marc Hérard (2) , Xavier Louis (3) , Gérard Poissant

1 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
2 EDF - EDF
3 IFSTTAR/COSYS/GRETTIA - Génie des Réseaux de Transport Terrestres et Informatique Avancée

This contribution's topic is the resolution of the hyperbolic system which describes a multicomponent turbulent ow. The model is written for an isentropic gas. We compute the exact solution of the Riemann Problem (RP) associated to the hyperbolic system. It is composed of constant states separated by rarefaction waves, or shock waves and a contact discontinuity. The selection of the admissible part of the shock curve is obtained by an entropic criterion. Compressive shock means entropic shock for only one of the two mathematical entropies found. This entropy is the total energy of the system. With these existence and uniqueness properties, we compute the exact solution of (RP) by a Smoller's kind of parameterization.

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

Emmanuelle Declercq, Alain Forestier, Jean-Marc Hérard, Xavier Louis, Gérard Poissant. An exact Riemann solver for multicomponent turbulent flow. International Journal of Computational Fluid Dynamics, 2001, 14, pp.117-131. ⟨10.1080/10618560008940719⟩. ⟨hal-01580049⟩