A divergence-free spectral expansions method for three-dimensional flows in spherical-gap geometries
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Regridding surface triangulations
Journal of Computational Physics
Convergence of a Boundary Integral Method for Water Waves
SIAM Journal on Numerical Analysis
Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique
SIAM Journal on Scientific Computing
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
Adaptive triangulation of evolving, closed, or open surfaces by the advancing-front method
Journal of Computational Physics
An efficient algorithm for hydrodynamical interaction of many deformable drops
Journal of Computational Physics
Spectral methods in MatLab
An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence
Journal of Computational Physics
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
A front-tracking method for the computations of multiphase 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
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Simulating the dynamics and interactions of flexible fibers in Stokes flows
Journal of Computational Physics
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
A high-order algorithm for obstacle scattering in three dimensions
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
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Algorithm for direct numerical simulation of emulsion flow through a granular material
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Short Note: A fast and stable method for rotating spherical harmonic expansions
Journal of Computational Physics
Journal of Computational Physics
A spectral boundary integral method for flowing blood cells
Journal of Computational Physics
Journal of Computational Physics
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
Accuracy and Stability of Computing High-order Derivatives of Analytic Functions by Cauchy Integrals
Foundations of Computational Mathematics
A finite-element/boundary-element method for large-displacement fluid-structure interaction
Computational Mechanics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend the study of Veerapaneni et al. [S.K. Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows, Journal of Computational Physics 228 (19) (2009) 7233-7249] to general non-axisymmetric vesicle flows in three dimensions. Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is needed to ensure stability of the time-stepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere. By introducing these algorithmic components, we obtain a time-stepping scheme that circumvents the stability constraint on the time-step and achieves spectral accuracy in space. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.