GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Second kind integral equation formulation of Stokes' flows past a particle of arbitary shape
SIAM Journal on Applied Mathematics
Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
A BEM-BDF scheme for curvature driven moving Stokes flows
Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
An efficient algorithm for hydrodynamical interaction of many deformable drops
Journal of Computational Physics
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Journal of Scientific Computing
Journal of Computational Physics
Dynamics of multicomponent vesicles in a viscous fluid
Journal of Computational Physics
Applying a second-kind boundary integral equation for surface tractions in Stokes flow
Journal of Computational Physics
Efficient numerical methods for multiple surfactant-coated bubbles in a two-dimensional stokes flow
Journal of Computational Physics
Hi-index | 31.48 |
We present new, highly accurate, and efficient methods for computing the motion of a large number of two-dimensional closed interfaces in a slow viscous flow. The interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex-variable theory for the biharmonic equation. The numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole-based iterative solution procedure, which requires only O(N) operations where N is the number of nodes in the discretization of the interface. The interface is described spectrally, and we use evolution equations that preserve equal arclength spacing of the marker points. We assume that the fluid on one side of the interface is inviscid and we discuss two different physical phenomena: bubble dynamics and interfacial motion driven by surface tension (viscous sintering). Applications from buoyancy-driven bubble interactions, the motion of polydispersed bubbles in an extensional flow, and the removal of void spaces through viscous sintering are considered and we present large-scale, fully resolved simulations involving O(100) closed interfaces.