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Article Dans Une Revue Networks and Heterogeneous Media Année : 2010

Small solids in an inviscid fluid

Résumé

We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. The coupling is ensured through a drag force that can be linear or quadratic. Though this model can be considered as a simple one, its mathematical analysis is involved. We put forward a notion of entropy solution to our model, define a Riemann solver and make first steps towards well-posedness results. The main goal is to construct easy-to-implement and yet reliable numerical approximation methods; we design several finite volume schemes, which are analyzed and tested.

Dates et versions

hal-00590617 , version 1 (04-05-2011)

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Boris Andreianov, Frédéric Lagoutière, Nicolas Seguin, Takéo Takahashi. Small solids in an inviscid fluid. Networks and Heterogeneous Media, 2010, 5 (3), pp.385-404. ⟨10.3934/nhm.2010.5.385⟩. ⟨hal-00590617⟩
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