A Lagrangian analysis of the gravity-inertial oil spreading on the calm sea using the reflective oil-water interface treatment

Negative impacts are caused by oil spills on coastal ecosystems. In the phenomenon of oil spreading, the knowledge of the physical properties of the pollutant, such as velocities and positions, is of fundamental importance for the adoption of timely contingency measures to protect the environment (Fraga Filho, Smoothed Particle Hydrodynamics: Fundamentals and Basic Applications in Continuum Mechanics, 2019). This paper presents a Lagrangian particle modelling for the prediction of the oil slick diameter in the first stage of the oil spreading on a calm sea. At the first studies on the oil spreading (Fay, The Spread of Oil Slicks on a Calm Sea, 1969; Fay, Physical Processes in the Spread of Oil on a Water Surface, 1971), curves were adjusted to laboratory experimental data. The modelling employed in this work is based on the continuum Navier-Stokes equations, and the Smoothed Particle Hydrodynamics (SPH) method has been used to obtain the solution for the conservation equations of mass and momentum. The oil-water interface was treated using a reflective treatment. The solution achieved was compared to the oil slick diameter predicted by Fay's equation, and an error lower than 1% was found.