Nonlinear Diffussion-Advection-Reaction Phenomena Involved in the Pumping of Oil from Open Sea: Modeling and Numerical Simulation.

Abstract

The main goal of this article is to improve upon a previous model used to simulate the evolution of oil spots in the open sea and the effect of a skimmer ship pumping oil out of the spots. The concentration of the pollutant is subject to the effects of wind and sea currents, diffusion, and the pumping action of a skimmer (i.e., cleaning) ship that follows a pre-assigned trajectory. This implies that the mathematical model is of the advection-reaction-diffusion type. A drawback of our previous model was that diffusion was propagating with infinite velocity; in this article, we use an improved modeling relying on a nonlinear diffusion term, implying that diffusion propagates with finite velocity. To reduce numerical diffusion when approximating the advection part of the model, we consider second order discretization schemes with nonlinear flux limiters. We consider also absorbing boundary conditions to insure accurate results near the boundary. Finally, to reduce CPU time we use an operator-splitting scheme for the time discretization. The novel approach we advocate in this article is validated by comparing our numerical results with real life measurements from the Prestige oil spill which took place in Spain in 2002.