New efficient time-stepping schemes for the anisotropic phase-field dendritic crystal growth model
| dc.rights.license | open | en_US |
| dc.contributor.author | LI, Minghui | |
| hal.structure.identifier | Institut de Mécanique et d'Ingénierie [I2M] | |
| dc.contributor.author | AZAIEZ, Mejdi | |
| dc.contributor.author | XU, Chuanju | |
| dc.date.accessioned | 2023-03-20T09:23:17Z | |
| dc.date.available | 2023-03-20T09:23:17Z | |
| dc.date.issued | 2022-03-01 | |
| dc.identifier.issn | 0898-1221 | en_US |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/172364 | |
| dc.description.abstractEn | In this paper, we propose and analyze a first-order and a second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed schemes are based on an auxiliary variable approach for the Allen-Cahn equation and delicate treatment of the terms coupling the Allen-Cahn equation and temperature equation. The idea of the former is to introduce suitable auxiliary variables to facilitate construction of high order stable schemes for a large class of gradient flows. We propose a new technique to treat the coupling terms involved in the crystal growth model, and introduce suitable stabilization terms to result in totally decoupled schemes, which satisfy a discrete energy law without affecting the convergence order. A delicate implementation demonstrates that the proposed schemes can be realized in a very efficient way. That is, it only requires solving four linear elliptic equations and a simple algebraic equation at each time step. A detailed comparison with existing schemes is given, and the advantage of the new schemes is emphasized. As far as we know this is the first second-order scheme that is totally decoupled, linear, unconditionally stable for the dendritic crystal growth model with variable mobility parameter. | |
| dc.language.iso | EN | en_US |
| dc.subject.en | Dendritic crystal growth | |
| dc.subject.en | Phase-field | |
| dc.subject.en | Time-stepping schemes | |
| dc.subject.en | Unconditional stability | |
| dc.title.en | New efficient time-stepping schemes for the anisotropic phase-field dendritic crystal growth model | |
| dc.title.alternative | Computers & Mathematics with Applications | en_US |
| dc.type | Article de revue | en_US |
| dc.identifier.doi | 10.1016/j.camwa.2022.01.017 | en_US |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Matériaux | en_US |
| bordeaux.journal | Computers & Mathematics with Applications | en_US |
| bordeaux.page | 204-215 | en_US |
| bordeaux.volume | 109 | en_US |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | en_US |
| bordeaux.institution | Université de Bordeaux | en_US |
| bordeaux.institution | Bordeaux INP | en_US |
| bordeaux.institution | CNRS | en_US |
| bordeaux.institution | INRAE | en_US |
| bordeaux.institution | Arts et Métiers | en_US |
| bordeaux.peerReviewed | oui | en_US |
| bordeaux.inpress | non | en_US |
| hal.identifier | hal-04037009 | |
| hal.version | 1 | |
| hal.date.transferred | 2023-03-20T09:23:20Z | |
| hal.export | true | |
| dc.rights.cc | Pas de Licence CC | en_US |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Computers%20&%20Mathematics%20with%20Applications&rft.date=2022-03-01&rft.volume=109&rft.spage=204-215&rft.epage=204-215&rft.eissn=0898-1221&rft.issn=0898-1221&rft.au=LI,%20Minghui&AZAIEZ,%20Mejdi&XU,%20Chuanju&rft.genre=article |
