Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations
| hal.structure.identifier | Institut de Recherche en Génie Civil et Mécanique [GeM] | |
| dc.contributor.author | CHINESTA, Francisco | |
| hal.structure.identifier | Institut de Recherche en Génie Civil et Mécanique [GeM] | |
| dc.contributor.author | ABISSET, Emmanuelle | |
| hal.structure.identifier | Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA] | |
| dc.contributor.author | AMMAR, Amine | |
| hal.structure.identifier | Aragón Institute of Engineering Research [Zaragoza] [I3A] | |
| dc.contributor.author | CUETO, Elías | |
| dc.date.accessioned | 2021-05-14T09:55:30Z | |
| dc.date.available | 2021-05-14T09:55:30Z | |
| dc.date.issued | 2015-04-30 | |
| dc.identifier.issn | 1815-2406 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/77700 | |
| dc.description | The fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed. | |
| dc.description.abstractEn | The fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed. | |
| dc.language.iso | en | |
| dc.publisher | Global Science Press | |
| dc.subject.en | Boltzmann equation | |
| dc.subject.en | Fokker-Planck equation | |
| dc.subject.en | proper gene | |
| dc.subject.en | multidimensional models | |
| dc.subject.en | convective stabilization | |
| dc.title.en | Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4208/cicp.2014.m326 | |
| dc.subject.hal | Informatique [cs]/Ingénierie assistée par ordinateur | |
| bordeaux.journal | Communications in Computational Physics | |
| bordeaux.page | 975-1006 | |
| bordeaux.volume | 17 | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01206757 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01206757v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Computational%20Physics&rft.date=2015-04-30&rft.volume=17&rft.issue=4&rft.spage=975-1006&rft.epage=975-1006&rft.eissn=1815-2406&rft.issn=1815-2406&rft.au=CHINESTA,%20Francisco&ABISSET,%20Emmanuelle&AMMAR,%20Amine&CUETO,%20El%C3%ADas&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||