A self-regularising DVM–PSE method for the modelling of diffusion in particle methods

Type Article
Date 2013-09
Language English
Author(s) Mycek Paul1, 2, Pinon Gregory1, Germain GregoryORCID2, Rivoalen Elie1, 3
Affiliation(s) 1 : Univ Havre, Lab Ondes & Milieux Complexes, CNRS, UMR 6294, F-76058 Le Havre, France.
2 : IFREMER, Marine Struct Lab, F-62321 Boulogne, France.
3 : INSA Rouen, Lab Optimisat & Firibilite Mecan Struct, EA 3828, F-76801 St Etienne, France.
Source Comptes Rendus Mecanique (1631-0721) (Elsevier France-editions Scientifiques Medicales Elsevier), 2013-09 , Vol. 341 , N. 9-10 , P. 709-714
DOI 10.1016/j.crme.2013.08.002
WOS© Times Cited 3
Keyword(s) Particle method, Diffusion, DVM, PSE
Abstract The modelling of diffusive terms in particle methods is a delicate matter and several models have been proposed in the literature. The Diffusion Velocity Method (DVM) consists in rewriting these terms in an advective way, thus defining a so-called diffusion velocity. In addition to the actual velocity, it is used to compute the particles displacement. On the other hand, the well-known and commonly used Particle Strength Exchange method (PSE) uses an approximation of the Laplacian operator in order to model diffusion. This approximation is based on an exchange of particles strength.

Although DVM is particularly well suited to particle methods since it preserves their Lagrangian aspect, its major drawback stems in the fact that it suffers from severe singular behaviours. This paper intends to give insights and ideas for coping with these issues, based on an exact decomposition of the diffusion coefficient allowing a hybrid DVM–PSE treatment of diffusive terms.
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