Essentially non-oscillatory schemes applied to Buckley-Leverett equation with diffusive term

The purpose of this work was to investigate the flow of two-phase fluids via the Buckley-Leverett equation, corresponding to three types of scenarios applied in oil extraction, including a diffusive term. For this, a weighted essentially non-oscillatory scheme, a Runge-Kutta method and a central finite difference were computationally implemented. In addition, a numerical study related to the precision order and stability was performed. The use of these methods made it possible to obtain numerical solutions without oscillations and without excessive numerical dissipation, sufficient to assist in the understanding of the mixing profiles of saturated water and petroleum fluids, inside pipelines filled with porous material, in addition to allowing the investigation of the impact of adding the diffusive term in the original equation.