Chebyshev pseudospectral solution of the Stokes equations using finite element preconditioning
Journal of Computational Physics
Wavy Taylor-vortex flows via multigrid-continuation methods
Journal of Computational Physics
Krylov methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Vorticity boundary condition and related issues for finite difference schemes
Journal of Computational Physics
Numerical methods for bifurcations of dynamical equilibria
Numerical methods for bifurcations of dynamical equilibria
A Simultaneous Iteration Algorithm for Real Matrices
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Newton-Krylov continuation of periodic orbits for Navier-Stokes flows
Journal of Computational Physics
Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems
Journal of Computational Physics
Global two-dimensional stability of the staggered cavity flow with an HOC approach
Computers & Mathematics with Applications
Hi-index | 31.46 |
An efficient numerical bifurcation and continuation method for the Navier-Stokes equations in cylindrical geometries is presented and applied to a nontrivial fluid dynamics problem, the flow in a cylindrical container driven by differential rotation. The large systems that result from discretizing the Navier-Stokes equations, especially in regimes where inertia is important, necessitate the use of iterative solvers which in turn need preconditioners. We use incomplete lower-upper decomposition (ILU) as an effective preconditioner for such systems and show the significant gain in efficiency when an incomplete LU of the full Jacobian is used instead of using only the Stokes operator. The computational cost, in terms of CPU time, grows with the size of the system (i.e., spatial resolution) according to a power law with exponent around 1.7, which is very modest compared to direct methods, indicating the appropriateness of the schemes for large nonlinear partial differential equation problems.