From continuum mechanics to SPH particle systems and back: systematic derivation and convergence
| Autor: | Evers, Joep H. M., Zisis, Iason A., van der Linden, Bas J., Duong, Manh Hong |
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| Přispěvatelé: | Center for Analysis, Scientific Computing & Appl. |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Technology
Science & Technology MASS EVOLUTION PROBLEM Applied Mathematics Mathematics Applied FOS: Physical sciences principle of least action COMPRESSIBLE FLUIDS Mathematical Physics (math-ph) Mechanics CONNECTION 09 Engineering MODEL convergence rate Smoothed Particle Hydrodynamics FLUX BOUNDARY-CONDITIONS measure-valued equations PRINCIPLES Physical Sciences 70H25 28A33 65M12 35Q70 46E27 70Fxx 76M25 Wasserstein distance Mathematics 01 Mathematical Sciences Mathematical Physics |
| Zdroj: | Zeitschrift für Angewandte Mathematik und Mechanik, 98(1), 106-133. Wiley-VCH Verlag |
| ISSN: | 0044-2267 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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