1. A method for simulating the two-dimensional invicid subsonic flows, comprising the following steps: (1) transforming the two-dimensional unsteady Euler equations in Euler plane to the Euler equations in Lagrangian formulation in Lagrangian plane; (2) reading object geometry for providing points on a surface of an object; (3) establishing a computational mesh around said object; and (4) solving the Euler equations in Lagrangian formulation in Lagrangian plane using the Strang-dimensional-splitting scheme with hybrid upwind flux operators.