After looking for a convenient definition of accuracy for finite-volume schemes on structured meshes, a high-order accurate scheme is constructed for the Euler equations. Thanks to suitably weighted discretization operators, the proposed scheme is third-order on mildly deformed grids and second-order on highly deformed grids. The influence of mesh deformations on the scheme accuracy is studied theoretically and numerically. Numerical results are shown for a Lamb vortex, subsonic flow past a cylinder and transonic flow past a NACA0012 airfoil. $ % & # '$ ( $
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