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An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids
dc.contributor.author | Peco Regales, Christian |
dc.contributor.author | Arroyo Balaguer, Marino |
dc.contributor.author | Rosolen, Adrian Martin |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2013-09-09T08:32:24Z |
dc.date.created | 2013-09 |
dc.date.issued | 2013-09 |
dc.identifier.citation | Peco, C.; Arroyo, M.; Rosolen, A. An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids. "Journal of computational physics", Setembre 2013, vol. 249, núm. 5, p. 320-336. |
dc.identifier.issn | 0021-9991 |
dc.identifier.uri | http://hdl.handle.net/2117/20106 |
dc.description.abstract | We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phasefield tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phasefield as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D. |
dc.format.extent | 17 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
dc.subject.lcsh | Membranes (Biology) -- Mathematical models |
dc.subject.other | Adaptivity |
dc.subject.other | Biomembranes |
dc.subject.other | Meshfree methods |
dc.subject.other | Phase field models |
dc.subject.other | Variational methods |
dc.subject.other | Vesicles |
dc.title | An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids |
dc.type | Article |
dc.subject.lemac | Membranes (Biologia) |
dc.contributor.group | Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
dc.identifier.doi | 10.1016/j.jcp.2013.04.038 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0021999113003239?via%3Dihub |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 12673342 |
dc.description.version | Postprint (published version) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/240487/EU/Predictive models and simulations in nano- and biomolecular mechanics: a multiscale approach/PREDMODSIM |
dc.date.lift | 10000-01-01 |
local.citation.author | Peco, C.; Arroyo, M.; Rosolen, A. |
local.citation.publicationName | Journal of computational physics |
local.citation.volume | 249 |
local.citation.number | 5 |
local.citation.startingPage | 320 |
local.citation.endingPage | 336 |
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