AUROUX , Didier

International audience

International audience

Images des Mathématiques, Les échos de la recherche

International audience

International audience

International audience

In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surfac e height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple non-linear observer which takes advantage of the symmetries of fluid dynamics laws. As a result its...

International audience

In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or...

International audience

In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surfac e height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple non-linear observer which takes advantage of the symmetries of fluid dynamics laws. As a result its...

International audience

International audience

In this paper, we first focus our interest on the use of the variational adjoint method in a relatively simple ocean model in order to try to reconstruct the four-dimensional ocean system from altimetric surface observations of the ocean.

In this Note, we introduce a new algorithm for data assimilation problems, called the back and forth nudging (BFN) algorithm. The standard forward nudging algorithm is first studied for a linear ODE model. The backward nudging algorithm is then introduced in order to reconstruct the initial state of the system. These two algorithms are combined...

International audience

This paper deals with a new data assimilation algorithm, called Back and Forth Nudging. The standard nudging technique consists in adding to the equations of the model a relaxation term that is supposed to force the observations to the model. The BFN algorithm consists in repeatedly performing forward and backward integrations of the model with...

In this paper, we generalize the so-called "nudging" algorithm in order to identify the initial condition of a dynamical system from experimental observations.

National audience

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We consider a multidimensional model of a compressible fluid in a bounded domain. We want to estimate the density and velocity of the fluid, based on the observations for only velocity. We build an observer exploiting the symmetries of the fluid dynamics laws. Our main result is that for the linearized system with full observations of the...

In this paper we describe a new variational approach for the detection of fine structures in an image (like filaments in 2D). This approach is based on the computation of the topological gradient associated to a cost function defined from a regu- larized version of the data (possibly noisy and / or blurred). We get this approximation by solving...

In this paper, we propose an improvement to the Back and Forth Nudging algorithm for handling diffusion in the context of geophysical data assimilation. We detail the Diffusive Back and Forth Nudging algorithm, in which the sign of the diffusion term is changed in the backward integrations. We study the convergence of this algorithm, in...

Data assimilation consists in estimating the state of a system by combining via numerical methods two different sources of information: models and observations. Data assimilation makes it possible to answer a wide range of questions such as: optimal identification of the initial state of a system, perform reliable numerical forecasts, identify...