AN EXACT RESCALING VELOCITY METHOD FOR SOME KINETIC FLOCKING MODELS

作者：Rey Thomas^*; Tan Changhui^*

来源：SIAM Journal on Numerical Analysis, 2016, 54(2): 641-664.

DOI：10.1137/140993430

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

In this work, we discuss kinetic descriptions of flocking models of the so-called Cucker-Smale [IEEE Trans. Automat. Control, 52 (2007), pp. 852-862] and Motsch-Tadmor [J. Statist. Phys., 144 (2011), pp. 923-947] types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range bi-particles interaction potentials. We introduce a new exact rescaling velocity method, inspired by the recent work [F. Filbet and T. Rey, T. Comput. Phys., 248 (2013) pp. 177-199], allowing us 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.

• 出版日期2016