Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

Type Article
Date 2016-07
Language English
Author(s) Mycek PaulORCID1, Pinon GregoryORCID2, Germain GregoryORCID3, Rivoalen Elie2, 4
Affiliation(s) 1 : Duke Univ, Dept Mech Engn & Mat Sci, 144 Hudson Hall,Box 90300, Durham, NC 27708 USA.
2 : Univ Havre, CNRS, UMR 6294, Lab Ondes & Milieux Complexes, 53 Rue Prony,BP 540, F-76058 Le Havre, France.
3 : IFREMER, Hydrodynam & Metocean Serv, 150 Quai Gambetta,BP 699, F-62321 Boulogne Sur Mer, France.
4 : INSA Rouen, EA 3828, Lab Optimisat & Fiabilite Mecan Struct, Ave Univ,BP 08, F-76801 St Etienne, France.
Source Computational & Applied Mathematics (0101-8205) (Springer Heidelberg), 2016-07 , Vol. 35 , N. 2 , P. 447-473
DOI 10.1007/s40314-014-0200-5
WOS© Times Cited 8
Keyword(s) Diffusion velocity method, Particle method, Fourier analysis, Transport-dispersion equations, Navier-Stokes equations
Abstract The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The diffusion velocity method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier–Stokes equations, in their incompressible, velocity–vorticity formulation. The integration of a large eddy simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.
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