GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
Spectral element multigrid. I. Formulation and numerical results
Journal of Scientific Computing
Grid independent convergence of the multigrid method for first-order equations
SIAM Journal on Numerical Analysis
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes
Journal of Computational Physics
An assessment of linear versus nonlinear multigrid methods for unstructured mesh solvers
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method
Journal of Scientific Computing
Short Note: An explicit expression for the penalty parameter of the interior penalty method
Journal of Computational Physics
Journal of Computational Physics
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
SIAM Journal on Scientific Computing
Efficient Solvers of Discontinuous Galerkin Discretization for the Cahn---Hilliard Equations
Journal of Scientific Computing
Hi-index | 31.45 |
Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations on unstructured meshes. The algorithms are based on coupling both p- and h-multigrid (ph-multigrid) methods which are used in nonlinear or linear forms, and either directly as solvers or as preconditioners to a Newton-Krylov method. The performance of the algorithms are examined in solving the laminar flow over an airfoil configuration. It is shown that the choice of the cycling strategy is crucial in achieving efficient and scalable solvers. For the multigrid solvers, while the order-independent convergence rate is obtained with a proper cycle type, the mesh-independent performance is achieved only if the coarsest problem is solved to a sufficient accuracy. On the other hand, the multigrid preconditioned Newton-GMRES solver appears to be insensitive to this condition and mesh-independent convergence is achieved under the desirable condition that the coarsest problem is solved using a fixed number of multigrid cycles regardless of the size of the problem. It is concluded that the Newton-GMRES solver with the multigrid preconditioning yields the most efficient and robust algorithm among those studied.