SIAM Journal on Scientific and Statistical Computing
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
The Method of Regularized Stokeslets
SIAM Journal on Scientific Computing
A Method for Computing Nearly Singular Integrals
SIAM Journal on Numerical Analysis
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Simulating the dynamics and interactions of flexible fibers in Stokes flows
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method
Journal of Computational Physics
An implicit immersed boundary method for three-dimensional fluid-membrane interactions
Journal of Computational Physics
Dynamics of multicomponent vesicles in a viscous fluid
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
Journal of Computational Physics
A fast, robust, and non-stiff Immersed Boundary Method
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We develop a numerical method for the coupled motion of Navier-Stokes flow with an elastic interface of zero thickness which exerts tension and bending forces on the fluid. The interface motion is made partially implicit by approximating a backward Euler step in the high wavenumbers as in the small scale decomposition method of Hou, Lowengrub and Shelley. This modified step is combined with the method of Beale and Layton [J.T. Beale, A.T. Layton, A velocity decomposition approach for moving interfaces in viscous fluids, J. Comput. Phys. 228 (2009) 3358-67]; the fluid velocity is found by computing the Stokes velocity and a more regular remainder. The resulting scheme is second order in space and first order in time; it can be made second order in time by extrapolation. The discontinuities in the pressure and velocity gradient are preserved. The partially implicit method allows much larger time steps than an explicit method with negligible added effort. The formulas in the Fourier transform for the implicit approximation in high wavenumbers are similar to those derived in Hou and Shi [T.Y. Hou, Z. Shi, An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, J. Comput. Phys. 227 (2008) 9138-69] in a different context.