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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:249

Article

Peco, C.¹  Rosolen, A.¹  Arroyo, M.¹ 

[1] Univ Politecn Cataluna, LaCaN, BarcelonaTech UPC, ES-08034 Barcelona, Spain

关键词: Phase field models;    Biomembranes;    Vesicles;    Meshfree methods;    Variational methods;    Adaptivity;   

DOI  :  10.1016/j.jcp.2013.04.038

来源: Elsevier

【 摘 要 】

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. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free