Analysis of the Convergence of Iterative Implicit and Defect-CorrectionAlgorithms for Hyperbolic Problems

摘要

The convergence of unfactored implicit schemes for the solution of the steadydiscrete Euler equations is studied using first and second order accurate discretizations simultaneously. The close resemblance of these schemes with iterative defect correction is shown. Linear model problems are introduced for the one dimensional and the two dimensional cases. These model problems are analyzed in detail both by Fourier by matrix analyses. The convergence behavior appears to be strongly dependent on a parameter that determines the amount of upwinding in the discretization of the second order scheme. The linear convection problem in one and two dimensions is studied in detail. Differences between the various cases are signaled. Experiments for the Euler equations are shown, including comments on how the theory is well or partially verified depending on the problem.