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An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids

Peco, C. ; Rosolen, A. ; Arroyo, M.

Journal of computational physics, 2013-09, Vol.249, p.320-336 [Periódico revisado por pares]

Elsevier Inc

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  • Título:
    An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids
  • Autor: Peco, C. ; Rosolen, A. ; Arroyo, M.
  • Assuntos: Adaptivity ; Algorithms ; Anàlisi numèrica ; Biomembranes ; Computational fluid dynamics ; Fluid flow ; Fluids ; Matemàtica aplicada a les ciències ; Matemàtiques i estadística ; Mathematical analysis ; Mathematical models ; Membranes (Biologia) ; Membranes (Biology) ; Meshfree methods ; Mètodes numèrics ; Phase field models ; Three dimensional ; Variational methods ; Vesicles ; Viscous fluids ; Àrees temàtiques de la UPC
  • É parte de: Journal of computational physics, 2013-09, Vol.249, p.320-336
  • Notas: ObjectType-Article-2
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  • Descrição: [Display omitted] •We propose a phase-field method to simulate membranes embedded in a viscous fluid.•The method is meshfree, Lagrangian, robust, and easily made parallel.•Adaptivity for free: the grid follows the sharp features of the solution.•A variational time integrator is developed, leading to a robust time-stepping strategy.•Dynamics are tested with large deformations and complex shape changes. 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 phase-field 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 phase-field 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.
  • Editor: Elsevier Inc
  • Idioma: Inglês
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