ORBi: Canor Thomas - Transient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics method

Reference : Transient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics ...


	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Multidisciplinary, general & others Engineering, computing & technology : Civil engineering
	To cite this reference:	http://hdl.handle.net/2268/134413

Title :	Transient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics method
Language :	English
Author, co-author :	Canor, Thomas [Université de Liège - ULg > Département ArGEnCo > Analyse sous actions aléatoires en génie civil >]
	Denoël, Vincent [Université de Liège - ULg > Département ArGEnCo > Analyse sous actions aléatoires en génie civil >]
Publication date :	May-2013
Journal title :	International Journal for Numerical Methods in Engineering
Publisher :	Wiley
Volume :	94
Issue/season :	6
Pages :	535–553
Peer reviewed :	Yes (verified by ORBi)
Audience :	International
ISSN :	0029-5981
e-ISSN :	1097-0207
City :	Chichester
Country :	United Kingdom
Keywords :	[en] Fokker-Planck equation ; Smoothed Particle Hydrodynamics ; Probabilistic methods ; Particle methods ; leapfrog euler ; Stochastic process
Abstract :	[en] Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function (pdf). The time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient Fokker-Planck-Kolmogorov equation (FPK). The FPK equation is a conservation equation of a hypothetical or abstract fluid, which models the transport of probability. This paper presents a generalized formalism for the resolution of the transient FPK equation using the well-known mesh-free Lagrangian method, Smoothed Particle Hydrodynamics (SPH). Numerical implementation shows notable advantages of this method in an unbounded state space: (i) the conservation of total probability in the state space is explicitly written, (ii) no artifact is required to manage far- eld boundary conditions , (iii) the positivity of the pdf is ensured and (iv) the extension to higher dimensions is straightforward. Furthermore, thanks to the moving particles, this method is adapted for a large kind of initial conditions, even slightly dispersed distributions. The FPK equation is solved without any a priori knowledge of the stationary distribution; just a precise representation of the initial distribution is required.
Funders :	Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Target :	Researchers
Permalink :	http://hdl.handle.net/2268/134413
DOI :	10.1002/nme

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