Environmental Modeling & Assessment

, Volume 17, Issue 3, pp 275–288

# Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution

• Quang A. Dang
• Matthias Ehrhardt
• Gia Lich Tran
• Duc Le
Article

## 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.

## Keywords

Oil transport problems Oil spilling Weathering Adjoint equation approach  Pollution source identification

## Mathematics Subject Classifications (2010)

62P12 65M06 65M32

## Notes

### 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

• Quang A. Dang
• 1
• Matthias Ehrhardt
• 2
• Gia Lich Tran
• 3
• Duc Le
• 4
1. 1.Institute of Information TechnologyHa noiVietnam
2. 2.Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C Mathematik und NaturwissenschaftenBergische Universität WuppertalWuppertalGermany
3. 3.Institute of MathematicsHa noiVietnam
4. 4.Buro of Hydrology and MeteorologyDang Thai ThanHa noiVietnam