GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Matrix computations (3rd ed.)
Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes
Journal of Computational Physics
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
An assessment of linear versus nonlinear multigrid methods for unstructured mesh solvers
Journal of Computational Physics
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Journal of Computational Physics
Journal of Computational Physics
An adaptive implicit-explicit scheme for the DNS and LES of compressible flows on unstructured grids
Journal of Computational Physics
Fast unsteady flow computations with a Jacobian-free Newton-Krylov algorithm
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
The efficiency gains obtained using higher-order implicit Runge-Kutta (RK) schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each time step are presented. The first algorithm (nonlinear multigrid, NMG) is a pseudo-time-stepping scheme which employs a nonlinear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the generalized minimal residual method. Results demonstrating the relative superiority of these Newton's method based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes such as fourth-order Runge-Kutta (RK64) with the more efficient inexact Newton's method based schemes (LMG).