An explicit well-balanced scheme on staggered grids for barotropic Euler equations

In this paper, we introduce a specific modification of the numerical fluxes in order to insure the well-balanced property of schemes on staggered grids for the Euler equations. This property is crucial for the numerical representation of equilibrium solutions of balance laws with source terms, like when describing flows subjected to gravity and a complex topography. We propose first and second order versions of the well-balanced scheme. The performances of the method are evaluated through a series of 1D and 2D benchmarks.