Name
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.3934/nhm.2010.5.385 | NETWORKS AND HETEROGENEOUS MEDIA |
Keywords | Field | DocType |
Solid-fluid interaction,Burgers equation,singular source term,adapted entropy,well-balanced scheme,random-choice method | Drag,Inviscid flow,Mathematical optimization,Ordinary differential equation,Mathematical analysis,Quadratic equation,Burgers' equation,Partial differential equation,Finite volume method,Mathematics,Riemann solver | Journal |
Volume | Issue | ISSN |
5 | 3 | 1556-1801 |
Citations | PageRank | References |
2 | 0.44 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Andreianov | 1 | 27 | 5.70 |
| Frédéric Lagoutière | 2 | 34 | 6.25 |
| Nicolas Seguin | 3 | 11 | 1.93 |
| Takéo Takahashi | 4 | 29 | 5.89 |