A computational model of aquatic animal locomotion
Journal of Computational Physics
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
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
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
Accurate projection methods for the incompressible Navier—Stokes equations
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
Journal of Computational Physics
Simulation of Swimming Organisms: Coupling Internal Mechanics with External Fluid Dynamics
Computing in Science and Engineering
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
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
Three-dimensional, fully adaptive simulations of phase-field fluid models
Journal of Computational Physics
A fast, robust, and non-stiff Immersed Boundary Method
Journal of Computational Physics
A boundary condition capturing immersed interface method for 3D rigid objects in a flow
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Hi-index | 31.48 |
The immersed boundary method is one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to require small time steps to maintain stability when solved with an explicit method. Many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability constraint, but none of them give satisfactory performance. In this paper, we propose an efficient semi-implicit scheme to remove this stiffness from the immersed boundary method for the Navier-Stokes equations. The construction of our semi-implicit scheme consists of two steps. First, we obtain a semi-implicit discretization which is proved to be unconditionally stable. This unconditionally stable semi-implicit scheme is still quite expensive to implement in practice. Next, we apply the small scale decomposition to the unconditionally stable semi-implicit scheme to construct our efficient semi-implicit scheme. Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit scheme 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. Our extensive numerical experiments show that our semi-implicit scheme has much better stability property than an explicit scheme. This offers a substantial computational saving in using the immersed boundary method.