Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier--Stokes Equations

We study preconditioners for the iterative solution of the linear systems arising in the implicit time integration of the compressible Navier-Stokes equations. The spatial discretization is carried out using a Discontinuous Galerkin method with fourth order polynomial interpolations on triangular elements. The time integration is based on backward difference formulas resulting in a nonlinear system of equations which is solved at each timestep. This is accomplished using Newton's method. The resulting linear systems are solved using a preconditioned GMRES iterative algorithm. We consider several existing preconditioners such as block-Jacobi and Gauss-Seidel combined with multi-level schemes which have been developed and tested for specific applications. While our results are consistent with the claims reported, we find that these preconditioners lack robustness when used in more challenging situations involving low Mach numbers, stretched grids or high Reynolds number turbulent fl...

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Per-Olof Persson, Jaime Peraire
• Keywords: Coarse Scale Correction, Low Mach Number, Preconditioner, SIAMSC 2008