Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Continuum models of platelet aggregation: formulation and mechanical properties
SIAM Journal on Applied Mathematics
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 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
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
Journal of Computational Physics
Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow
Journal of Computational Physics
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Proteus: a direct forcing method in the simulations of particulate flows
Journal of Computational Physics
Simulation of fluid slip at 3D hydrophobic microchannel walls by the lattice Boltzmann method
Journal of Computational Physics
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An iterative matrix-free method in implicit immersed boundary/continuum methods
Computers and Structures
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
The immersed boundary method: A projection approach
Journal of Computational Physics
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
Journal of Computational Physics
Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations
Mathematics and Computers in Simulation
Journal of Computational Physics
On numerical modeling of animal swimming and flight
Computational Mechanics
Computers & Mathematics with Applications
Hi-index | 0.09 |
The immersed boundary method is a practical and effective method for fluid-structure interaction problems. It has been applied to a variety of problems. Most of the time-stepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary force is computed at the unknown configuration of the structure at each time step. The fully nonlinear algebraic system resulting from discretizations is solved by an Inexact Newton-Krylov method in a Jacobian-free manner. The test problem of a flexible filament in a flowing viscous fluid is considered. Numerical results show that the proposed implicit immersed boundary method is much more stable with larger time steps and significantly outperforms the explicit version in terms of computational cost.