TY - JOUR
T1 - An adaptive meshfree method for phase-field models of biomembranes. Part II
T2 - A Lagrangian approach for membranes in viscous fluids
AU - Peco, C.
AU - Rosolen, A.
AU - Arroyo, M.
N1 - Funding Information:
We acknowledge the support of the European Research Council under the European Community’s 7th Framework Programme (FP7/2007-2013)/ERC grant agreement nr 240487, and of the Ministerio de Ciencia e Innovacin (DPI2011-26589). MA acknowledges the support received through the prize “ICREA Academia” for excellence in research, funded by the Generalitat de Catalunya. CP acknowledges FPI-UPC Grant, FPU Ph. D. Grant (Ministry of Science and. Innovation, Spain) and Collegi d’Enginyers de Camins, Canals i Ports de Catalunya for their support.
PY - 2013/9/5
Y1 - 2013/9/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jcp.2013.04.038
DO - 10.1016/j.jcp.2013.04.038
M3 - Article
AN - SCOPUS:84879413405
VL - 249
SP - 320
EP - 336
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -