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From continuum mechanics to SPH particle systems and back: systematic derivation and convergence
- Source :
- Zeitschrift für Angewandte Mathematik und Mechanik, 98(1), 106-133. Wiley-VCH Verlag
- Publication Year :
- 2018
-
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.
- Subjects :
- 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
Subjects
Details
- Language :
- English
- ISSN :
- 00442267
- Database :
- OpenAIRE
- Journal :
- Zeitschrift für Angewandte Mathematik und Mechanik, 98(1), 106-133. Wiley-VCH Verlag
- Accession number :
- edsair.doi.dedup.....82cd4e74103632569c251fab1dd9c2dc