GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific and Statistical Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
Krylov methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
Mathematics of Computation
A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
Journal of Computational Physics
SIAM Journal on Matrix Analysis and Applications
Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method
SIAM Journal on Matrix Analysis and Applications
Multigrid
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Predicting the onset of flow unsteadiness based on global instability
Journal of Computational Physics
A relaxation method for large eigenvalue problems, with an application to flow stability analysis
Journal of Computational Physics
Journal of Computational Physics
Efficient evaluation of the direct and adjoint linearized dynamics from compressible flow solvers
Journal of Computational Physics
Hi-index | 31.46 |
The combination of iterative Krylov-based eigenvalue algorithms and direct numerical simulations (DNS) has proven itself an effective and robust tool in solving complex global stability problems of compressible flows. A Cayley transformation is required to add flexibility to our stability solver and to allow access to specific parts of the full global spectrum which would be out of reach without such a transformation. In order to robustify the overall global stability solver an efficient ILU-based preconditioner has been implemented. With this Cayley-transformed DNS-based Krylov method two flow cases were successfully investigated: (i) a compressible mixing layer, a rather simple but well-known problem, which served as a test case and (ii) a supersonic flow about a swept parabolic body, a challenging large-scale flow configuration.