Data assimilation and pollution forecasting in Burgers' equation with model error function |
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Authors: | Tran Thu Ha Nguyen Hong Phong François-Xavier Le Dimet Hong Son Hoang |
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Institution: | 1. Institute of Mechanics, 264 Doi Can, Graduate University of Science and Technology, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, University of Engineering and Technology, VNU, 144 Xuan Thuy, Hanoï, Viet Nam;2. Laboratoire Jean-Kuntzmann, 51, rue des Maths, 38400 Saint-Martin-d''Hères, France;3. REC/HOM/SHOM, 42, avenue Gaspard-Coriolis, 31000 Toulouse, France |
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Abstract: | This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence. |
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Keywords: | Corresponding author Burgers' equation Water pollution Data assimilation Optimal method BFGS Équation de Burgers Pollution de l'eau Assimilation de données Méthode optimale BFGS |
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