Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations

  • Authors:

  • Amir Nejat;Carl Ollivier-Gooch

  • Affiliations:

  • Department of Mechanical Engineering, The University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, Canada BC V6T 1Z4;Department of Mechanical Engineering, The University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, Canada BC V6T 1Z4

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

Quantified Score

Hi-index 31.47

Visualization

Abstract

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton-Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower-upper factorization (LU) and an incomplete lower-upper factorization (ILU(4)) techniques are employed for preconditioning of the resultant linear system. The solver performance and the conditioning of the preconditioned linear system have been compared in detail for second, third, and fourth-order accuracy. The conditioning and eigenvalue spectrum of the preconditioned system are examined to investigate the quality of preconditioning.