A SPH multiphase formulation with a surface tension model applied to oil-water separation

A SPH model [1] addressing the specific issue of accurately evaluating the quantities which are discontinuous across the interface is used to simulate multiphase flows together with the presence of a free surface (meaning here an interface without accounting for the (air) phase above it). This work is an extension of the formulation discussed in [2] and it is based on the variational approach introduced by [3]. Physical models have been added in the formulation to account for viscous and surface tension effects. Classical tests for which reference solutions are available in literature are used to validate the latter models, such as the Poiseuille flow or an oscillating droplet without gravity. More complex validation case is then simulated such as an air bubble rising by gravity in a water column at rest. Finally, the model capabilities are illustrated on the case of a simplified oil-water separator.