Comparison of matrix-free acceleration techniques in compressible Navier-Stokes calculations

Six different preconditioning methods to accelerate the convergence rate of Krylov-subspace iterative methods are described, implemented and compared in the context of matrix-free techniques. The acceleration techniques comprehend Krylov-subspace iterative methods; invariant subspace-based methods and matrix approximations: Jacobi, LU-SGS, Deflated GMRES; Augmented GMRES; polynomial preconditioner and FGMRES/Krylov. The relative behaviour of the methods is explained in terms of the spectral properties of the resulting iterative matrix. The employed code uses a Newton–Krylov approach to iteratively solve the Euler or Navier–Stokes equations, for a supersonic ramp or a viscous compressible double-throat flow. The linear system approximate solver is the GMRES method, in either the restarted or FGMRES variants. The results show the better performance of the methods that approximate the iterative matrix, such as Jacobi, LU-SGS and FGMRES/Krylov