A computational model of aquatic animal locomotion
Journal of Computational Physics
Journal of Computational Physics
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
Interaction of oscillating filaments: a computational study
Journal of Computational Physics
A computational model of the cochlea using the immersed boundary method
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Stability analysis for the immersed fiber problem
SIAM Journal on Applied Mathematics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Simulating the motion of flexible pulp fibres using the immersed boundary method
Journal of Computational Physics
Computational methods for continuum models of platelet aggregation
Journal of Computational Physics
Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Two-Dimensional Simulations of Valveless Pumping Using the Immersed Boundary Method
SIAM Journal on Scientific Computing
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
Journal of Computational Physics
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
Simulation of Swimming Organisms: Coupling Internal Mechanics with External Fluid Dynamics
Computing in Science and Engineering
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
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
A fast, robust, and non-stiff Immersed Boundary Method
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Hi-index | 31.49 |
The immersed boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the immersed boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semi-implicit schemes to remove this stiffness from the immersed boundary method for the two-dimensional Stokes flow. First, we obtain a novel unconditionally stable semi-implicit discretization for the immersed boundary problem. Using this unconditionally stable discretization as a building block, we derive several efficient semi-implicit schemes for the immersed boundary problem by applying the small scale decomposition to this unconditionally stable discretization. Our stability analysis and extensive numerical experiments show that our semi-implicit schemes offer much better stability property than the explicit scheme. Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit schemes can be solved explicitly in the spectral space. Thus the computational cost of our semi-implicit schemes is comparable to that of an explicit scheme, but with a much better stability property.