An Exact Rescaling Velocity Method for some Kinetic Flocking Models

Abstract : 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.
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SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, 54 (2), pp.641-664. <10.1137/140993430.>
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Thomas Rey, Changhui Tan. An Exact Rescaling Velocity Method for some Kinetic Flocking Models. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, 54 (2), pp.641-664. <10.1137/140993430.>. <hal-01078298v2>

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