Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
An analysis of the fractional step method
Journal of Computational Physics
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Vortex methods with spatially varying cores
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
Analysis of an exact fractional step method
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
A fixed-mesh method for incompressible flow-structure systems with finite solid deformations
Journal of Computational Physics
Dynamically coupled fluid-body interactions in vorticity-based numerical simulations
Journal of Computational Physics
A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers
Journal of Computational Physics
Sources of spurious force oscillations from an immersed boundary method for moving-body problems
Journal of Computational Physics
Numerically stable fluid-structure interactions between compressible flow and solid structures
Journal of Computational Physics
Journal of Computational Physics
An improved penalty immersed boundary method for fluid-flexible body interaction
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
Towards oscillation-free implementation of the immersed boundary method with spectral-like methods
Journal of Computational Physics
A novel iterative direct-forcing immersed boundary method and its finite volume applications
Journal of Computational Physics
An accurate moving boundary formulation in cut-cell methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An immersed boundary method for two-fluid mixtures
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.57 |
A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion. Like previous methods, a boundary force is applied at the immersed surface to satisfy the no-slip constraint. This extra constraint can be added to the incompressible Navier-Stokes equations by introducing regularization and interpolation operators. The current method gives prominence to the role of the boundary force acting as a Lagrange multiplier to satisfy the no-slip condition. This role is analogous to the effect of pressure on the momentum equation to satisfy the divergence-free constraint. The current immersed boundary method removes slip and non-divergence-free components of the velocity field through a projection. The boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger CFL numbers compared to some past methods. Symmetry and positive-definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field. Examples show that the current formulation achieves second-order temporal accuracy and better than first-order spatial accuracy in L"2-norms for one- and two-dimensional test problems. Results from two-dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies.