A bounded upwind-downwind semi-discrete scheme for finite volume methods for phase separation problems

Abstract

Phase separation processes play a key role in many industrial applications. For instance, the oil industry is full of examples of surface installations devoted to separate water from oil just after the extracted mixture leaves the well. Phase separation problems pose many challenges to numerical schemes due to the presence of shock and rarefaction waves, typical of hyperbolic problems. Moreover, the transported variables, usually the fractions of each of the phases present in the mixture, have the additional important feature of being bounded, for only fractions between 0 and 1 have physical meaning. The numerical schemes should be able to deal with this restriction, avoiding unrealistic, non-physical fraction values.