SOLVING THE UNIFORM DENSITY CONSTRAINT IN A DOWNSCALING STOCHASTIC MODEL
Claire Chauvin, Sever A. Hirstoaga, P. Kabelikova, Antoine Rousseau, Mireille Bossy · 2007
In a collaboration with the french national agency for development of ecol- ogy and energy control (ADEME), we intend to build a new numerical method to com- pute small scale phenomena in atmospheric models, getting rid of any mesh refinement. In an existing mesh, we virtually drop some particles that are moved thanks to a sys- tem of Stochastic Dierential Equations adapted from S.B. Pope. We then estimate local values of the required fields, thanks to the computation of a mean value over an ensemble of particles. We are thus using Monte-Carlo methods, and aim to study their convergence rates, and finally compare them to classical refinement methods. One (con- tastable) constraint of Pope's model is the uniform value of the density ( = cst). That is, the particles have to be uniformly distributed at every time step. This particular problem is the framework of our CEMRACS project. We aim to use D.P. Bertsekas Auction Algorithm in order to move a given cloud of particles to a new position, which is also given in advance, and that realizes the constraint = cst. Naturally, the trans- port cost will have to be minimum. This is a problem of 3D optimal transport, which is known to be dicult.