Abstract
In this paper, we present an isogeometric analysis for studying the dynamical behavior of inextensible vesicles under an external fluid flow with inertial forces. We consider a phase-field model Aland, et al. (2014) for the coupled fluid–vesicle problem which enforces global area and volume constraints using a Lagrange multiplier method and employs an extra equation for enforcing local inextensibility condition. Full Navier–Stokes equations are considered and their finite element formulation is presented based on a residual-based variational multiscale method while a standard Galerkin finite element framework is employed for the rest of partial differential equations in the model. We solve the system of PDEs using an implicit, monolithic scheme based on the generalized-α time integration method. Compared to the system of equations considered in Aland, et al. (2014), we reduce the number of equations to be solved by leveraging high continuity of NURBS functions. We also extend the algorithm of the phase-field method to three-dimensional problems. A number of two-dimensional numerical examples which model the dynamics of a vesicle in a quiescent fluid, in a shear flow, and in plane Poiseuille flow with and without obstructions are studied. The resistive immersed surface method is employed for dealing with obstructions. We also consider a 3D example where we study the dynamics of a vesicle in a constricted channel which resembles the situation that a vesicle experiences in a stenosed microchannel.
•We present a monolithic, implicit formulation based on isogeometric analysis and generalized-alpha time integration for simulating hydrodynamics of vesicles according to a phase-field model.•The number of equations of the phase-field model that need to be solved is reduced by leveraging high continuity of NURBS functions, and the algorithm is extended to 3D.•We introduce the RIS method into the formulation which can be employed for an implicit description of complex geometries using a diffuse–interface approach.•The implementation highlights the robustness of the RBVMS method for Navier–Stokes equations of incompressible flows with non-trivial localized forcing terms including bending and tension forces of the vesicle.•The potential of the phase-field model for accurate simulation of a variety of fluid–vesicle interaction problems in 2D and 3D is demonstrated.