A computational model of aquatic animal locomotion
Journal of Computational Physics
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
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
Modeling biofilm processes using the immersed boundary method
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Journal of Computational Physics
An adaptive version of the immersed boundary method
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
The blob projection method for immersed boundary problems
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
Approximate Projection Methods: Part I. Inviscid Analysis
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
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
On computational issues of immersed finite element methods
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
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
A multirate time integrator for regularized Stokeslets
Journal of Computational Physics
Journal of Computational Physics
A fast, robust, and non-stiff Immersed Boundary Method
Journal of Computational Physics
Computers & Mathematics with Applications
A boundary condition capturing immersed interface method for 3D rigid objects in a flow
Journal of Computational Physics
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
A study of different modeling choices for simulating platelets within the immersed boundary method
Applied Numerical Mathematics
Journal of Computational Physics
Hi-index | 31.52 |
The immersed boundary (IB) method is known to require small timesteps to maintain stability when solved with an explicit or approximately implicit method. Many implicit methods have been proposed to try to mitigate this timestep restriction, but none are known to be unconditionally stable, and the observed instability of even some of the fully implicit methods is not well understood. In this paper, we prove that particular backward Euler and Crank-Nicolson-like discretizations of the nonlinear immersed boundary terms of the IB equations in conjunction with unsteady Stokes Flow can yield unconditionally stable methods. We also show that the position at which the spreading and interpolation operators are evaluated is not relevant to stability so as long as both operators are evaluated at the same location in time and space. We further demonstrate through computational tests that approximate projection methods (which do not provide a discretely divergence-free velocity field) appear to have a stabilizing influence for these problems; and that the implicit methods of this paper, when used with the full Navier-Stokes equations, are no longer subject to such a strict timestep restriction and can be run up to the CFL constraint of the advection terms.