Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Convergence of a Boundary Integral Method for Water Waves
SIAM Journal on Numerical Analysis
On the numerical evaluation of electrostatic fields in dense random dispersions of cylinders
Journal of Computational Physics
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
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
Numerical methods for multiple inviscid interfaces in creeping flows
Journal of Computational Physics
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 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
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
A fast multipole method for the three-dimensional Stokes equations
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Journal of Computational Physics
Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
Journal of Computational Physics
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
A level set projection model of lipid vesicles in general flows
Journal of Computational Physics
Petaflop biofluidics simulations on a two million-core system
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.51 |
We present a new method for the evolution of inextensible vesicles immersed in a Stokesian fluid. We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the non-local hydrodynamic forces with the elastic forces due to bending and tension. Numerical simulations of such vesicle motions are quite challenging. On one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives and a milder constraint due to a transport-like stability condition. On the other hand, an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step. We present two semi-implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme. We discretize the equations by using a spectral method in space, and a multistep third-order accurate scheme in time. We use the fast multipole method (FMM) to efficiently compute vesicle-vesicle interaction forces in a suspension with a large number of vesicles. We report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme.