Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems

摘要: This paper studies the convergence of unfactored implicit schemes for solution steady discrete Euler equations. In these first and second order accurate discretisations are simultaneously used. The close resemblance with iterative defect correction is shown. Linear model problems introduced one-dimensional two-dimensional cases. These analyzed in detail both by Fourier matrix analyses. behaviour appears to be strongly dependent on a parameter b that determines amount upwinding discretisation scheme. general, iteration, after an impulsive phase slower pseudo-convective (or Fourier) can distinguished finally again faster asymptotic phase. extreme values = 0 (no upwinding) 1 (full appear as special cases which degenerates. They not recommended practical use. For intermediate value pseudo-convection less significant. Fromm's scheme (b 1/2) or Van Leer's third 1/3) show quite satisfactory behaviour. this paper, linear convection problem one two dimensions studied detail. Differences between various signalized. last section experiments shown equations, including comments how theory well partially verified depending problem.