Convergence acceleration of iterative solutions of Euler equations for transonic flow computations (Q1821659)

Two acceleration techniques for Euler calculations are investigated. The first technique is an extrapolation procedure based on the power method; it is applicable when the iterative matrix has dominant eigenvalues. Both real and complex conjugate roots are allowed. The second technique is a generalization of the minimal residual method, where the extrapolation step consists of a weighted combination of the corrections at different iteration levels and the weights are chosen to minimize the \(L_ 2\)-norm of the residual. Numerical results, using Jameson's Runge-Kutta Multigrid Code [\textit{A. Jameson}, Appl. Math. Comput. 13, 327-355 (1983; Zbl 0545.76065)], are presented. The extra computational work to apply either technique is negligible and the extra storage is not a problem on current supercomputers.