Small solids in an inviscid fluid | Zendy

Boris Andreïanov | Zendy; Frédéric Lagoutìère | Zendy; Nicolas Seguin | Zendy; Takéo Takahashi | Zendy

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Small solids in an inviscid fluid

Author(s) -

Boris Andreïanov,

Frédéric Lagoutìère,

Nicolas Seguin,

Takéo Takahashi

Publication year - 2010

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2010.5.385

Subject(s) - inviscid flow , burgers' equation , riemann solver , partial differential equation , solver , mathematics , drag , quadratic equation , ordinary differential equation , differential equation , simple (philosophy) , mathematical analysis , finite volume method , classical mechanics , mathematical optimization , physics , mechanics , geometry , philosophy , epistemology

International audienceWe 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

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