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
SIAM Journal on Numerical Analysis
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
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
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
An immersed boundary method with direct forcing for the simulation of particulate flows
Journal of Computational Physics
Immersed boundary method for flow around an arbitrarily moving body
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
Journal of Computational Physics
The immersed boundary method: A projection approach
Journal of Computational Physics
Journal of Computational Physics
Short note: A note on pressure accuracy in immersed boundary method for Stokes flow
Journal of Computational Physics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational Physics
A novel iterative direct-forcing immersed boundary method and its finite volume applications
Journal of Computational Physics
A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions
Journal of Computational Physics
An accurate moving boundary formulation in cut-cell methods
Journal of Computational Physics
Journal of Computational Physics
On numerical modeling of animal swimming and flight
Computational Mechanics
Hi-index | 31.49 |
The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.