An explicit MUSCL scheme on staggered grids with kinetic-like fluxes for the barotropic and full Euler system

We present a second order scheme for the barotropic and full Euler equations. The scheme works on staggered grids, with numerical unknowns stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We identify stability conditions ensuring the positivity of the discrete density and energy. We illustrate the ability of the scheme to capture the structure of complex flows with 1d and 2d simulations on mac grids.