A finite volume technique for solving the twodimensional compressible Euler equations on multi-block structured grids is presented. The discretization of the advective derivatives is unconditionally second-order accurate thanks to a piecewise quadratic reconstruction of the conservative variables. An original implicit timeintegration is applied in order to improve the convergence to the steady state. At each time step, the unsteady Euler equations are solved using an Inexact New-ton method. The linear system arising from the New-ton linearization is solved by a point Jacobi method. The stability of the latter when dealing with high-order schemes is ensured by a Runge-Kutta multi-step algorithm. The multi-block strategy allows mesh discontinuiities through block-interfaces. Advantage can be taken from this flexibility in order to adapt the grid according to the main features of the flowfield. Efficiency of both finite volume scheme and implicit time-integration is illustrated on subsonic and transonic test cases.
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