Abstract: A Lagrangian finite point method for two-dimensional compressible hydrodynamics problems is presented.The numerical scheme is based on scattered points inside a computational domain without need for a specific connectivity.A cloud of five neighbors is selected around each point at each time step,and this cloud is used to implement finite point schemes based on five-point approximation formulas to gather information about flow derivatives.For numerical stability concerns,four artificial Laplace operators are introduced and added to corresponding conservative equations,respectively.Furthermore,an adaptive strategy for time step is also provided.Numerical results show validity and potential interest on this approach.

Key words: two dimensional compressible flow problems, Lagrangian finite point method, directional differences, meshfree method