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Some examples of kinetic schemes whose diffusion limit is Il’in’s exponential-fitting

  • Laurent Gosse
  • Nicolas Vauchelet
Article
  • 19 Downloads

Abstract

This paper is concerned with diffusive approximations of some numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov–Fokker–Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a “scattering S-matrix”, itself derived from a normal modes decomposition of the stationary solution. One common feature these models share is the type of diffusive approximation: their macroscopic densities solve drift-diffusion systems, for which a distinguished numerical scheme is Il’in/Scharfetter–Gummel’s “exponential fitting” discretization. We prove that these well-balanced schemes relax, within a parabolic rescaling, towards such type of discretization by means of an appropriate decomposition of the S-matrix, hence are asymptotic preserving.

Mathematics Subject Classification

65M06 34D15 76M45 76R50 

Notes

Acknowledgements

We gladly thank Prof. Christian Krattenthaller (Vienna) for his kind help in the study of the Haar property satisfied by exponential monomials.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Istituto per le Applicazioni del CalcoloRomeItaly
  2. 2.Laboratoire Analyse Géométrie et ApplicationsUniversité Paris 13, Sorbonne Paris Cité, CNRS UMR 7539VilletaneuseFrance

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