一种考虑界面不连续的改进的有限粒子法

The finite particle method(FPM) is an important improvement for the smoothed particle hydrodynamics(SPH) method, which effectively improves the calculation accuracy of boundary particles. However, when the discontinuous physical field is solved by the FPM, the accuracy in the vicinity of the discontinuous interface is greatly reduced, and the non-singularity of the matrix must be satisfied in the FPM, which requires an elaborate handling of the interface. Based on the discontinuous SPH(DSPH) method, this paper proposed an improved FPM-discontinuous special FPM(DSFPM), which considers the discontinuous interface, aiming to improve the computational accuracy at the interface and further improve the efficiency and stability of the FPM. In this paper, the estimation accuracy of the DSFPM was analyzed firstly, and then the algorithm flow diagram of the DSFPM to deal with the small deformation and large deformation problems was demonstrated. Next, the DSFPM, DSPH and FPM were used to simulate the small deformation problem-elastic aluminum blocks impact. By comparing the velocity and stress of the aluminum blocks and computational time, we verified the accuracy and computational efficiency of the DSFPM. Finally, the simulation of the large deformation problem was realized by a combining method with the DSFPM and DFPM.