A two-dimensional second order conservative front-tracking method with an original marker advection approach based on jump relations

A two-dimensional front-tracking method is developed for handling complex shape interfaces satisfying the volume conservation. In order to validate the proposed front-tracking method, a complete convergence study is carried out on several analytical test cases for which the interface is widely stretched and deformed. Comparisons to different existing approaches show that our front-tracking method is second order accurate in space with lower errors than existing interface tracking techniques of the literature. We also propose an original marker advection method which takes into account the jump relations valid at interface in order to deal with the contrast of physical properties encountered in two-phase flow simulations. The conservative front-tracking method computed in this work is shown to be able to describe interfaces with high accuracy even for poorly resolved Eulerian grids.