Review of incompressible fluid flow computations using the vorticity-velocity formulation
Applied Numerical Mathematics
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Developing high-order weighted compact nonlinear schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Journal of Computational Physics
A high-order fast direct solver for singular Poisson equation
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
Journal of Computational Physics
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
Journal of Computational Physics
Journal of Computational Physics
Proteus: a direct forcing method in the simulations of particulate flows
Journal of Computational Physics
Journal of Computational Physics
An immersed boundary method with direct forcing for the simulation of particulate flows
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
An immersed boundary method for complex incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
A new immersed boundary method based on vorticity-velocity formulations for the simulation of 2D incompressible viscous flow is proposed in present paper. The velocity and vorticity are respectively divided into two parts: one is the velocity and vorticity without the influence of the immersed boundary, and the other is the corrected velocity and the corrected vorticity derived from the influence of the immersed boundary. The corrected velocity is obtained from the multi-direct forcing to ensure the well satisfaction of the no-slip boundary condition at the immersed boundary. The corrected vorticity is derived from the vorticity transport equation. The third-order Runge-Kutta for time stepping, the fourth-order finite difference scheme for spatial derivatives and the fourth-order discretized Poisson for solving velocity are applied in present flow solver. Three cases including decaying vortices, flow past a stationary circular cylinder and an in-line oscillating cylinder in a fluid at rest are conducted to validate the method proposed in this paper. And the results of the simulations show good agreements with previous numerical and experimental results. This indicates the validity and the accuracy of present immersed boundary method based on vorticity-velocity formulations.