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Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution

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An Erratum to this article was published on 27 May 2012

Abstract

This paper deals with the mathematical modeling and algorithms for the problem of oil pollution. For solving this task, we derive the adjoint problem for the advection–diffusion equation describing the propagation of oil slick after an accident, which we call the main problem. We prove a fundamental equality between the solutions of the main and the adjoint problems. Based on this equality, we propose a novel method for the identification of the pollution source location and the accident time of oil emission. This approach is illustrated on an example for an accident in the offshore of the central part of the Vietnamese coast. Numerical simulations demonstrate the effectiveness of the proposed method. Besides, the method is verified for 1D model of substance propagation.

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Acknowledgements

This first two authors were supported partially by the bilateral German–Vietnamese project OILPOLL: Mathematical Modelling and Numerical Algorithms for Simulation of Oil Pollution, financed by the International Buro of the BMBF. The third author was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED).

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Authors and Affiliations

  1. Institute of Information Technology, 18 Hoang Quoc Viet, Ha noi, Vietnam

    Quang A. Dang

  2. Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstrasse 20, 42119, Wuppertal, Germany

    Matthias Ehrhardt

  3. Institute of Mathematics, 18 Hoang Quoc Viet, Ha noi, Vietnam

    Gia Lich Tran

  4. Buro of Hydrology and Meteorology, Dang Thai Than, Ha noi, Vietnam

    Duc Le

Authors
  1. Quang A. Dang
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  2. Matthias Ehrhardt
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  3. Gia Lich Tran
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  4. Duc Le
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Corresponding author

Correspondence to Matthias Ehrhardt.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10666-012-9324-4

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Dang, Q.A., Ehrhardt, M., Tran, G.L. et al. Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution. Environ Model Assess 17, 275–288 (2012). https://doi.org/10.1007/s10666-011-9291-1

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  • DOI: https://doi.org/10.1007/s10666-011-9291-1

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