Résumé
The present work aims to contribute to the development of a numerical method to compute small scale phenomena in atmospheric models, getting rid of any mesh refinement. In a domain, typically a mesh of a numerical weather prediction model, we simulate some particles that are moved thanks to a Stochastic Lagrangian model adapted from the PDF methods proposed by S.B. Pope. We estimate the Eulerian values of the required fields, thanks to the computation of a local mean value over an ensemble of particles. We are thus using a stochastic particle method. At small scale, our atmospheric model imposes that the mass density is constant in the domain. As a consequence, the particles have to be uniformly distributed at every time step of the particle method. We aim to use D.P. Bertsekas Auction algorithm in order to satisfy this constraint. Naturally, the transport cost will have to be minimum. This is a problem of 3D optimal transport, which is known to be difficult.