title: Advection modes by optimal mass transfer.
abstract: Classical model reduction techniques approximate the solution of a physical model by a limited number of global modes. These modes are usually determined by variants of principal component analysis. Global modes can lead to reduced models that perform well in terms of stability and accuracy. However, when the physics of the model is mainly characterized by advection, the nonlocal representation of the solution by global modes essentially reduces to a Fourier expansion. In this paper we describe a method to determine a low-order representation of advection. This method is based on the solution of Monge-Kantorovich mass transfer problems. Examples of application to point vortex scattering, Korteweg-de Vries equation, and hurricane Dean advection are discussed.
authors.affiliation: Institut de Mathématiques de Bordeaux, UMR 5251 CNRS, Université de Bordeaux, Inria Bordeaux, Sud Ouest, 33400 Talence, France.
authors.forename: Angelo
authors.initials: A
authors.lastname: Iollo
authors.affiliation: Inria Paris-Rocquencourt, B.P. 105 Domaine de Voluceau, 78153 Le Chesnay, France.
authors.forename: Damiano
authors.initials: D
authors.lastname: Lombardi