This paper is dedicated to a numerical method based on Glimm's idea and applied to the specific problem of advection of an indicator function. The numerical scheme relies on a fractional step approach for which: the first step is performed using any classical finite-volume scheme, and the second step sharpens the approximated solution issued from the first step. This second step is based on a random choice as proposed in the original idea of Glimm. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh-size. Since the method proposed in this paper naturally extends to multi-dimensional domain, both one- and two-dimensional cases have been considered
