Evaluation of the Numerical Method Runge-Kutta Used in the Oil Dispersion ECOS Model

Oil spill in the marine ecosystem is a problem that cause worries for the modern society. The oil spills generate multiple effects in different time scales: after the first hour, the effect is direct due the formation of a superficial layer and liberation of toxic compounds. On the other hand, in long term, processes like vertical dispersion and sedimentation can occur reaching levels that the problem became chronic and sometimes irreversible. The numerical modelling of these processes is an important tool with low economical cost, useful for analysis and forecasting of accidents. The numerical model developed at the Universidade Federal do Rio Grande (ECOS - Easy Coupling Oil System) is constantly modified in order to improve the simulations and make the results similar to real scenarios. In this sense, the aim of this work is use the numerical method Runge-Kutta to solve the differential equations and compare the results with the Euler method previously used by this model. The presented results indicate that there is a few difference in the displacement of the oil slick between the simulations where the Runge-Kutta of second and fourth order were employed. However, there is a high variation when these methods are compared with the Euler method which the oil are spreading more rapidly.