Boris Andreianov - Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25030 Besançon Cedex, France (email)
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.
interaction, Burgers equation, singular source
term, adapted entropy, well-balanced scheme, random-choice method.
Received: January 2010; Revised: June 2010; Published: July 2010.
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