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2010, Volume 5, Issue 3: 385-404. Doi: 10.3934/nhm.2010.5.385
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Small solids in an inviscid fluid

  • 1.

    Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25030 Besançon Cedex

  • 2.

    Laboratoire de mathématiques, Université Paris-Sud, 91405 Orsay cedex

  • 3.

    UMR 7598 Laboratoire J.-L. Lions, UPMC Univ Paris 06, Paris, F-75005

  • 4.

    Institut Élie Cartan UMR 7502, INRIA, Nancy-Université, CNRS, 54506 Vandoeuvre-lès-Nancy Cedex

Received:  December 31, 2009
Revised:  May 31, 2010
Published:  August 2010
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35F25, 35L80, 65M99.

    Citation:
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