Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique
SIAM Journal on Scientific Computing
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
Spectral methods in MatLab
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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
Finite element modeling of lipid bilayer membranes
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
Journal of Computational Physics
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
3D vesicle dynamics simulations with a linearly triangulated surface
Journal of Computational Physics
Applying a second-kind boundary integral equation for surface tractions in Stokes flow
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case-spectral approximation in space, semi-implicit time-stepping scheme-the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.