SIAM Journal on Scientific and Statistical Computing
Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
Journal of Computational Physics
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Vorticity boundary condition and related issues for finite difference schemes
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
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
Journal of Computational Physics
Finite difference schemes for incompressible flow based on local pressure boundary conditions
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
Journal of Computational Physics
Journal of Computational Physics
Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation
Journal of Computational Physics
A boundary condition capturing immersed interface method for 3D rigid objects in a flow
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
In the immersed interface method, a boundary immersed in a fluid is represented as a singular force in the Navier-Stokes equations. This paper presents an explicit approach for computing the singular force to enforce prescribed motion of a rigid boundary in an incompressible viscous flow. The tangential component of the singular force is related to the surface vorticity and is calculated from the normal derivative of the velocity. The normal component of the singular force is determined from a predictor and a corrector. The predictor uses the normal derivative of the vorticity. The corrector superposes a homogeneous solution to the pressure Poisson equation to achieve the desired normal derivative of the pressure. In the current immersed interface method, the velocity and the pressure are solved using the MAC scheme with the incorporation of jump conditions induced by the singular force and a discontinuous finite body force. The body force is applied to obtain the rigid motion of the fluid enclosed by the boundary. Circular Couette flow, flow past a cylinder, and flow around flappers are simulated to test the accuracy, stability, and efficiency of the method as well as the effect of the corrector. With no stiff springs to model rigid boundaries, the method is stable at relatively high Reynolds numbers.