GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
An efficient scheme for unsteady flow past an object with boundary conformal to a circle
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
A block-matrix iterative numerical method for coupled solving 2D Navier-Stokes equations
Journal of Computational Physics
Vorticity boundary condition and related issues for finite difference schemes
Journal of Computational Physics
Essentially compact schemes for unsteady viscous incompressible flows
Journal of Computational Physics
A high order explicit method for the computation of flow about a circular cylinder
Journal of Computational Physics
Discrete compatibility in finite difference methods for viscous incompressible fluid flow
Journal of Computational Physics
A Central-Difference Scheme for a Pure Stream Function Formulation of Incompressible Viscous Flow
SIAM Journal on Scientific Computing
| Hi-index | 31.45 |
We propose an efficient method for computing coupled flow-body dynamics. The time-stepping is implicit, and uses an iterative method (preconditioned GMRES) to solve the flow-body equations. The preconditioner solves a decoupled version of the equations which involves only the inversion of banded matrices, and requires a small number of iterations per time step. We use the method to probe the instability to horizontal motions of an elliptical body with simple vertical motions: flapping and rising. In both cases a linear instability to horizontal motion sets in above a critical Reynolds number, leading to a stable oscillatory state. The pressure forces play a destabilizing role against the stabilizing viscous forces, with oscillatory time scales set by either external flapping or the intrinsic flow-body coupling. The latter lowers the instability threshold in Reynolds number.