Taylor-SPH vs Taylor-Galerkin for shock waves in viscoplastic continua
DOI:
https://doi.org/10.13052/EJCM.20.281-308Keywords:
Taylor-SPH, Taylor-Galerkin, shock wave, viscoplastic, FEMAbstract
A new time discretization scheme with a corrected SPH is presented. The time discretization has been carried out by means of a Taylor series expansion in two steps. In order to avoid numerical instabilities, two different sets of particles have been considered in the time discretization, and a Lagrangian kernel has been used for the spatial approximation. The Lagrangian kernel and its gradient have been corrected to satisfy the consistency conditions. This new method is applied to solve the propagation of shock waves in elastoviscoplastic media and the results are compared with those obtained with a similar time discretization scheme within the frame of FEM. The proposed method is shown to be stable and robust. Numerical dispersion and diffusion are minimized and only a reduced number of particles is required to obtain reasonably accurate results.
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