Léa BATTEUX (LAMIA) : Anti-diffusive scheme for the transport of step functions

In this presentation, we discuss an anti-diffusive scheme for the transport of piecewise constant functions in space (type characteristic functions), generalising the Lagrange projection scheme to the case of transport by non-constant velocities. The advection equation is discretised by the Finite Volume Method on a staggered mesh, and a 3D variant verifying the maximum principle is obtained by alternating directions. This type of scheme makes it possible to consider, for example, the modelling of the movement of a bubble in a fluid or of several immiscible fluids.