Title: An immersed boundary method for simulating vesicle dynamics in three dimensions
Authors: Seol, Yunchang
Hu, Wei-Fan
Kim, Yongsam
Lai, Ming-Chih
Department of Applied Mathematics
Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
Keywords: Immersed boundary method;Incompressible membrane;Three-dimensional vesicle;Navier-Stokes equations
Issue Date: 1-Oct-2016
Abstract: We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows (Hu et al., 2014 [17]) to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric case, the fully 3D numerical implementation is much more complicated and is far from straightforward. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. As in 3D axisymmetric case, instead of keeping the vesicle locally incompressible, we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. The vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex (Lagrangian marker in the IB method) of the triangulation. A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method. We perform the convergence study for the immersed boundary forces and the fluid velocity field. We then study the vesicle dynamics in various flows such as quiescent, simple shear, and gravitational flows. Our numerical results show good agreements with those obtained in previous theoretical, experimental and numerical studies. (C) 2016 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jcp.2016.06.035
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2016.06.035
Volume: 322
Begin Page: 125
End Page: 141
Appears in Collections:Articles