GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
Numerical methods for multiple inviscid interfaces in creeping flows
Journal of Computational Physics
Simulating the dynamics and interactions of flexible fibers in Stokes flows
Journal of Computational Physics
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations
SIAM Journal on Scientific Computing
Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
Journal of Computational Physics
Applying a second-kind boundary integral equation for surface tractions in Stokes flow
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
SIAM Journal on Scientific Computing
Hi-index | 31.47 |
We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibility of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.