Abstract: In order to achieve accurate characterization of the process of tungsten alloy projectile penetrating the target, Finite Element Method (FEM), Smoothed Particle Galerkin (SPG), Smoothed Particle Hydrodynamics (SPH) and FE-SPH adaptive numerical simulation methods were used respectively to carry out numerical simulation calculation of tungsten alloy projectile penetrating Q235A steel target. The advantages and disadvantages of four numerical simulation methods in describing the residual velocity of the projectile, the perforation diameter of the target plate and the formation of secondary fragments after the projectile penetrates the target are compared. The results show that in terms of describing the residual velocity of the projectile, FEM method and FE-SPH adaptive method are strictly dependent on the selection of failure criteria and failure parameters because FEM method is based on the element erosion algorithm when dealing with the material failure problem. The SPG method is based on the bond fracture model when simulating material failure. The bond can be broken to simulate material failure without deleting SPG particles, and it is insensitive to failure parameters, so relatively accurate results can be obtained without adjusting failure parameters. In terms of describing the perforation diameter of the target plate, FEM and FE-SPH adaptive methods have accurate material boundaries and can accurately characterize the perforation morphology of the target plate, but the perforation diameter of the target plate varies greatly under different failure criteria. The SPH method is inferior to the SPG method in characterizing the perforation diameter of the target plate, and because the SPG method is not sensitive to the failure parameters, it can also accurately characterize the perforation diameter of the target plate. In terms of secondary fragment generation, FEM method can only generate large fragments, but not small fragments. The SPG method can characterize large and small fragments, but cannot output SPG particles as fragment information. Both FE-SPH adaptive method and SPH method can characterize large and small fragments, and the FE-SPH adaptive method can directly obtain the information of large fragments, but compared with the SPH method, the calculation efficiency is low.