Backward Calculation Based on the Advection and Diffusion of Oil Spills on the Sea Surface

Advection and diffusion equation is an effective means of investigating the motional state of oil spills. Common study is based on the known initial and boundary conditions to calculate the equation onwards. Unlike previous works, in this paper we focus on backward calculating advection and diffusion equation, namely, starting computation from the moment when the oil spill is found back to the moment when the incident occurs. Through such a simulation, we hope to trace the track of oil spills …

Backward Calculation Based on the Advection and Diffusion of Oil Spills on the Sea Surface

In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & diffusion equation, on the one hand, the advection term itself has the strong unilateral property, which means information in the upper reaches is transmitted downstream via the advection term; on the other hand, because of the opposite direction of calculation, it is essential for information to be conveyed upstream by means of the advection term. In addition, unlike that in the forward calculation, the diffusion term in the backward calculation is prone to accumulate errors, and thus renders the whole scheme unstable. Therefore, we adopt the central difference to deal with both the convectional term and the diffusion term. By examining two practical examples (1) under the unlimited boundary condition, and (2) under the limited boundary condition, it is proven that this method could achieve fundamentally satisfactory results not only in the open ocean but also in the closed or semi-closed bay.