A high-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows

  • Authors:

  • Amir Nejat;Carl Ollivier-Gooch

  • Affiliations:

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

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

Quantified Score

Hi-index 31.48

Visualization

Abstract

A fast implicit Newton-Krylov finite volume algorithm has been developed for high-order unstructured steady-state computation of inviscid compressible flows. The matrix-free generalized minimal residual (GMRES) algorithm is used for solving the linear system arising from implicit discretization of the governing equations, avoiding expensive and complex explicit computation of the high-order Jacobian matrix. The solution process has been divided into two phases: start-up and Newton iterations. In the start-up phase an approximate solution with the general characteristics of the steady-state flow is computed by using a defect correction procedure. At the end of the start-up phase, the linearization of the flow field is accurate enough for steady-state solution, and a quasi-Newton method is used, with an infinite time step and very rapid convergence. A proper limiter implementation for efficient convergence of the high-order discretization is discussed and a new formula for limiting the high-order terms of the reconstruction polynomial is introduced. The accuracy, fast convergence and robustness of the proposed high-order unstructured Newton-Krylov solver for different speed regimes is demonstrated for the second, third and fourth-order discretization. The possibility of reducing computational cost required for a given level of accuracy by using high-order discretization is examined.