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From continuum mechanics to SPH particle systems and back : systematic derivation and convergence
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Evers, Joep H. M., Zisis, Iason A., Linden, Bas J. van der and Duong, Manh Hong (2018) From continuum mechanics to SPH particle systems and back : systematic derivation and convergence. ZAMM - Journal of Applied Mathematics and Mechanics, 98 (1). pp. 106-133. ISSN 1521-4001.
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WRAP-continuum-mechanics-SPH-particle-systems-back-Duong-2017.pdf - Accepted Version - Requires a PDF viewer. Download (1232Kb) | Preview |
Official URL: https://doi.org/10.1002/zamm.201600077
Abstract
In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which regularization and the principle of least action are applied. We obtain two different equations, whose discrete counterparts coincide with the scheme used traditionally in the Smoothed Particle Hydrodynamics (SPH) numerical method (e.g. Monaghan), and with the equation treated by Di Lisio et al., respectively. Additionally, we prove the convergence in the Wasserstein distance of the corresponding measure-valued evolutions, moreover providing the order of convergence of the SPH method. The convergence holds for a general class of force fields, including external and internal conservative forces, friction and non-local interactions. The proof of convergence is illustrated numerically by means of one and two-dimensional examples.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Physics |
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| Journal or Publication Title: | ZAMM - Journal of Applied Mathematics and Mechanics | ||||||||
| Publisher: | Wiley | ||||||||
| ISSN: | 1521-4001 | ||||||||
| Official Date: | January 2018 | ||||||||
| Dates: |
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| Volume: | 98 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 106-133 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 29 June 2017 | ||||||||
| Date of first compliant Open Access: | 14 August 2018 |
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