A simple 1D model of inviscid fluid-solid interaction

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:245

Article

Lagoutiere, Frederic^2,3  Seguin, Nicolas¹  Takahashi, Takeo⁴ 

[1] Univ Paris 06, LJLL, UMR 7598, F-75252 Paris 05, France

[2] Univ Paris Diderot, F-75252 Paris, France

[3] CNRS, UMR 7598, Lab Jacques Louis Lions, F-75252 Paris 05, France

[4] Nancy Univ, CNRS, INRIA, Inst Elie Cartan UMR 7502, F-54506 Vandoeuvre Les Nancy, France

关键词: Burgers equation;    Fluid-particle interaction;    Riemann problem;    Non-conservative product;   

DOI  :  10.1016/j.jde.2008.03.011

来源: Elsevier

【 摘 要 】

We analyze a one-dimensional fluid-particle interaction model, composed by the Burgers equation for the fluid velocity and an ordinary differential equation which governs the particle movement. The coupling is achieved through a friction term. One of the novelties is to consider entropy weak solutions involving shock waves. The difficulty is the interaction between these shock waves and the particle. We prove that the Riemann problem with arbitrary data always admits a solution, which is explicitly constructed. Besides, two asymptotic behaviors are described: the long-time behavior and the behavior for large friction coefficients. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free