Comptes Rendus
no. 9-10
A self-regularising DVM–PSE method for the modelling of diffusion in particle methods
Paul Mycek1, 2 ; Grégory Pinon1  ; Grégory Germain2 ; Élie Rivoalen1, 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
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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crme.2013.08.002
Mots clés : 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 
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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. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.08.002/

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