## Section: New Results

### Velocity space transformations: collisional case

Participants : Emmanuel Franck, Philippe Helluy [correspondent] , Laurent Navoret.

The method of "velocity space transformations" allows to obtain an interesting discretization of the Kinetic equations like Vlasov-Poisson or Vlasov Maxwell equations as has been proved in the works of P. Helluy, L. Navoret and N. Pham. During this year, we have begun to extend this method to the collisional case using the entropy variable to write a general collisional operator. To treat all the regimes (small or large collisional regime), asymptotic preserving schemes (stability and convergence independent of the collisional frequency) have been designed. However, this method admits some numerical difficulties if we use the physical entropy to construct the collisional operator. Now we propose to use modified entropy, which has good numerical properties and gives limit regime close to the real one in the low Mach context. If this new approach gives interesting results, we will study the adaptivity of the velocity discrete basis which would allow to treat the collisional and non-collisional regimes with the same method.