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## Section: New Results

### A MUSCL–scheme on staggered grids with kinetic–like fluxes for the barotropic Euler system

Participants : Julia Llobell, Thierry Goudon, Sebastian Minjeaud.

We set up a MUSCL version of the scheme introduced in [27] for solving the barotropic Euler equations. The scheme works on staggered grids, with numerical densities and velocities stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We have identified stability conditions for the second order method and have shown the ability of the scheme to capture the structure of complex flows with 2D simulations on MAC grids.