Comptes Rendus
A self-regularising DVM–PSE method for the modelling of diffusion in particle methods
Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 709-714.

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.

Published online:
DOI: 10.1016/j.crme.2013.08.002
Keywords: Particle method, Diffusion, DVM, PSE

Paul Mycek 1, 2; Grégory Pinon 1; Grégory Germain 2; Élie Rivoalen 1, 3

1 Laboratoire Ondes et milieux complexes, UMR 6294, CNRS–université du Havre, 53, rue de Prony, BP 540, 76058 Le Havre cedex, France
2 IFREMER, Marine Structures Laboratory, 150, quai Gambetta, BP 699, 62321 Boulogne-Sur-Mer, France
3 Laboratoire dʼoptimisation et fiabilité en mécanique des structures, EA 3828, INSA de Rouen, avenue de lʼUniversité, BP 08, 76801 Saint-Étienne-du-Rouvray, France
     author = {Paul Mycek and Gr\'egory Pinon and Gr\'egory Germain and \'Elie Rivoalen},
     title = {A self-regularising {DVM{\textendash}PSE} method for the modelling of diffusion in particle methods},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {709--714},
     publisher = {Elsevier},
     volume = {341},
     number = {9-10},
     year = {2013},
     doi = {10.1016/j.crme.2013.08.002},
     language = {en},
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AU  - Grégory Germain
AU  - Élie Rivoalen
TI  - A self-regularising DVM–PSE method for the modelling of diffusion in particle methods
JO  - Comptes Rendus. Mécanique
PY  - 2013
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PB  - Elsevier
DO  - 10.1016/j.crme.2013.08.002
LA  - en
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%0 Journal Article
%A Paul Mycek
%A Grégory Pinon
%A Grégory Germain
%A Élie Rivoalen
%T A self-regularising DVM–PSE method for the modelling of diffusion in particle methods
%J Comptes Rendus. Mécanique
%D 2013
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Paul Mycek; Grégory Pinon; Grégory Germain; Élie Rivoalen. A self-regularising DVM–PSE method for the modelling of diffusion in particle methods. Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 709-714. doi : 10.1016/j.crme.2013.08.002.

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