Riemann problem for a particle-fluid coupling

Nina Aguillon (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a discontinuous function and a Dirac measure. After defining the solution, we solve the Riemann problem with a fixed particle for arbitrary data. We exhibit a set of condition on the drag force under which there exists a unique self-similar solution.

Mots clés: Fluid-particle interaction; Euler equations; Riemann problem; nonconservative product.; nonconservative product

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Nina Aguillon. Riemann problem for a particle-fluid coupling. Mathematical Models and Methods in Applied Sciences, 2015, http://www.worldscientific.com/doi/abs/10.1142/S0218202515500025. ⟨hal-00916234v2⟩