Comparison Study of Implicit Gauss-Seidel Line Iteration Method for Transonic Flows

Abstract

This paper studies the sweep direction efiect on the convergence rate and CPU time of the implicit unfactored Gauss-Seidel line relaxation (GSLR) method for compressible ∞ows. The line Gauss-Seidel iteration is also compared with the LU-SGS (lower-upper symmetric Gauss-Seidel) method. A modifled LU-SGS method, namely LU-GSLR, is studied. The LU-GSLR use the unfactored GSLR method with the simple matrix of the LU-SGS. The numerical experiments indicate that for the external ∞ows, the line Gauss-Seidel relaxation methods with sweeping in all directions achieves the optimum convergence rate and CPU e‐ciency. For an inviscid transonic internal ∞ow, the best convergence rate is obtained with sweeping in streamwise direction only. Within each time step, one sweep (a forward sweep plus a backward sweep) per time step is su‐cient. For the three implicit methods, GSLR, LU-SGS, and LU-GSLR, the GSLR is the most e‐cient method when the Roe scheme is used. The LU-GSLR method is a feasible method and can achieve better e‐ciency than the LU-SGS for some cases.