This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretization. In order to avoid numerical instabilities, two different sets of particles are used in the time discretization. To validate the Taylor-SPH method, it has been applied to solve the propagation of shock waves in elastic materials and the results have been compared with those obtained with a corrected SPH discretization combined with a 4th order Runge-Kutta time integration. The Taylor-SPH method is shown to be stable, robust and efficient and it provides more accurate results than those obtained with the standard SPH along with the Runge-Kutta time integration scheme. Numerical dispersion and diffusion are eliminated and only a reduced number of particles is required to obtain accurate results.
| Published in | Applied and Computational Mathematics (Volume 4, Issue 4) |
| DOI | 10.11648/j.acm.20150404.17 |
| Page(s) | 286-295 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Taylor-SPH (TSPH), Meshfree, Runge-Kutta, Shock Wave, Stability, Dynamics
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APA Style
H. Idder, M. Mabssout, M. I. Herreros. (2015). The Taylor-SPH Meshfree Method: Basis and Validation. Applied and Computational Mathematics, 4(4), 286-295. https://doi.org/10.11648/j.acm.20150404.17
ACS Style
H. Idder; M. Mabssout; M. I. Herreros. The Taylor-SPH Meshfree Method: Basis and Validation. Appl. Comput. Math. 2015, 4(4), 286-295. doi: 10.11648/j.acm.20150404.17
AMA Style
H. Idder, M. Mabssout, M. I. Herreros. The Taylor-SPH Meshfree Method: Basis and Validation. Appl Comput Math. 2015;4(4):286-295. doi: 10.11648/j.acm.20150404.17
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Download@article{10.11648/j.acm.20150404.17,
author = {H. Idder and M. Mabssout and M. I. Herreros},
title = {The Taylor-SPH Meshfree Method: Basis and Validation},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {4},
pages = {286-295},
doi = {10.11648/j.acm.20150404.17},
url = {https://doi.org/10.11648/j.acm.20150404.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150404.17},
abstract = {This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretization. In order to avoid numerical instabilities, two different sets of particles are used in the time discretization. To validate the Taylor-SPH method, it has been applied to solve the propagation of shock waves in elastic materials and the results have been compared with those obtained with a corrected SPH discretization combined with a 4th order Runge-Kutta time integration. The Taylor-SPH method is shown to be stable, robust and efficient and it provides more accurate results than those obtained with the standard SPH along with the Runge-Kutta time integration scheme. Numerical dispersion and diffusion are eliminated and only a reduced number of particles is required to obtain accurate results.},
year = {2015}
}
TY - JOUR T1 - The Taylor-SPH Meshfree Method: Basis and Validation AU - H. Idder AU - M. Mabssout AU - M. I. Herreros Y1 - 2015/07/02 PY - 2015 N1 - https://doi.org/10.11648/j.acm.20150404.17 DO - 10.11648/j.acm.20150404.17 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 286 EP - 295 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20150404.17 AB - This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretization. In order to avoid numerical instabilities, two different sets of particles are used in the time discretization. To validate the Taylor-SPH method, it has been applied to solve the propagation of shock waves in elastic materials and the results have been compared with those obtained with a corrected SPH discretization combined with a 4th order Runge-Kutta time integration. The Taylor-SPH method is shown to be stable, robust and efficient and it provides more accurate results than those obtained with the standard SPH along with the Runge-Kutta time integration scheme. Numerical dispersion and diffusion are eliminated and only a reduced number of particles is required to obtain accurate results. VL - 4 IS - 4 ER -
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