An Exact Rescaling Velocity Method for some Kinetic Flocking Models
This work provides a numerical method for efficiently simulating flocking dynamics in kinetic models, which is relevant for researchers studying collective behavior.
The authors developed an exact rescaling velocity method for simulating kinetic flocking models (Cucker-Smale and Motsch-Tadmor types) that avoids remeshing or fine velocity grids, and introduced a stabilized upwind finite volume scheme preserving momentum conservation.
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.