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We have developed a front-tracking method for compressible fluids(described by the Euler system),which is within the ALE framework,runs on general quadrangular grids,and is based on the conservation properties of the fluids.The method allows the interface to cut grid cells,and inside the cut cells the locations of the interface segments are computed using the conservation properties of the fluids.Numerical results show that the method can simulate interfaces with large deformation.