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Abstract: In this paper, we present a method to compute compressible flows in 2D. It uses two steps: a Lagrangian step and a metric-based triangular mesh adaptation step. Computational mesh is locally adapted according to some metric field that depends on physical or geometrical data. This mesh adaptation step embeds a conservative remapping procedure to satisfy consistency with Euler equations. The whole method is no more Lagrangian. After describing mesh adaptation patterns, we recall the metric formalism. Then, we detail an appropriate remapping procedure which is first-order and relies on exact intersections. We give some hints about the parallel implementation. Finally, we present various numerical experiments which demonstrate the good properties of the algorithm. [ABSTRACT FROM AUTHOR]