Title :

An Exact Rescaling Velocity Method for some Kinetic Flocking Models

Author(s) :

Rey, Thomas [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Tan, Changhui [Auteur]
Center for Scientific Computation and Mathematical Modeling [CSCAMM]

Journal title :

SIAM Journal on Numerical Analysis

Pages :

641–664

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2016

ISSN :

0036-1429

English keyword(s) :

rescaling velocity methods
kinetic equations
flocking models
finite volume methods
large time behavior
upwind scheme

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only ...
Show more >In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range bi-particles interaction potential. We introduce a new exact rescaling velocity method, inspired by a recent work of Filbet and Rey, allowing to observe numerically the flocking behavior of the solutions to these equations, without a need of remeshing or taking a very fine grid in the velocity space. To stabilize the exact method, we also introduce a modification of the classical upwind finite volume scheme which preserves the physical properties of the solution, such as momentum conservation.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

21 pages, 6 figures

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL