Solving the Uniform Density Constraint in a Stochastic Downscaling Model

Claire Chauvin 1 Sever Adrian Hirstoaga 2 Pavla Kabelikova 3 Antoine Rousseau 1 Frédéric Bernardin 4 Mireille Bossy 5
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
5 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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.
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Claire Chauvin, Sever Adrian Hirstoaga, Pavla Kabelikova, Antoine Rousseau, Frédéric Bernardin, et al.. Solving the Uniform Density Constraint in a Stochastic Downscaling Model. CEMRACS 2007 - Centre d'Eté Mathématique de Recherche Avancée en Calcul Scientifique, Aug 2007, Marseille, France. pp.97-110, ⟨10.1051/proc:2008032⟩. ⟨inria-00326931⟩

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