GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A stability analysis of incomplete LU factorizations
Mathematics of Computation
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
An implicit upwind algorithm for computing turbulent flows on unstructured grids
Computers and Fluids
A fast, matrix-free implicity method for compressible flows on unstructured grids
Journal of Computational Physics
Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
SIAM Journal on Scientific Computing
Comparison of several spatial discretizations for the Navier-Stokes equations
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
International Journal of High Performance Computing Applications
Journal of Computational Physics
Fast unsteady flow computations with a Jacobian-free Newton-Krylov algorithm
Journal of Computational Physics
Estimating Computational Noise
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
Despite becoming increasingly popular in many branches of computational physics, Jacobian-free Newton-Krylov (JFNK) methods have not become the approach of choice in the solution of the compressible Navier-Stokes equations for turbulent aerodynamic flows. To a degree, this is related to some subtle aspects of JFNK methods that are not well understood, and, if poorly handled, can lead to inefficient and unreliable performance. These are described here, along with strategies for addressing them, leading to an efficient JFNK algorithm for turbulent aerodynamic flows applicable to multi-block structured grids and a one-equation turbulence model. Development of globalization strategies for field-equation turbulence models represents one of the key contributions of the paper. Numerous examples of subsonic and transonic flows over single and multi-element airfoils are presented in order to demonstrate the efficiency and reliability of the algorithm. In addition, a number of guidelines are presented to aid in diagnosing problems with JFNK algorithms.