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dc.contributor.authorPeco Regales, Christian
dc.contributor.authorArroyo Balaguer, Marino
dc.contributor.authorRosolen, Adrian Martin
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.identifier.citationPeco, 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.description.abstractWe 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.extent17 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.lcshMembranes (Biology) -- Mathematical models
dc.subject.otherMeshfree methods
dc.subject.otherPhase field models
dc.subject.otherVariational methods
dc.titleAn adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids
dc.subject.lemacMembranes (Biologia)
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.description.peerreviewedPeer Reviewed
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/240487/EU/Predictive models and simulations in nano- and biomolecular mechanics: a multiscale approach/PREDMODSIM
local.citation.authorPeco, C.; Arroyo, M.; Rosolen, A.
local.citation.publicationNameJournal of computational physics

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