An improved SPH method in the discontinuous interface problem

It is necessary to introduce the discontinuous SPH method because discontinuous physical quantities often appear in SPH numerical simulations. Based on Taylor series expansion, discontinuous SPH expressions in 2D and 3D simulations were derived. For the computation of discontinuous physical quantities at material interface with large deformations, how to determine discontinuous locations was presented, and the method to determine x_k in discontinuous formulas was proposed theoretically based on Taylor series expansion and validated numerically. Initial SPH method, CSPM method and the discontinuous SPH method were compared and discussed when simulating discontinuous quantities. The results show that the discontinuous SPH method is more attractive when simulating discontinuous quantities.