APPLICATION OF PRECONDITIONED CONJUGATE GRADIENT-LIKE METHODS TO TWO AND THREE DIMENSIONAL FLUID FLOW CALCULATIONS

Abstract

Performance evaluation of the preconditioned conjugate gradient-like methods is made through the numerical simulation of two and three dimensional turbulent flow fields with the finite volume method. Preconditioned solvers examined include conjugate gradient method (PCG), conjugate residual method (PCR), bi-conjugate gradient method (PBCG) and conjugate gradient squared method (PCGS). Comparisons of the performance of the solvers demonstrate that the combination of PCG for the pressure-correction equation and PCR for the other equations requires the least CPU time against both two and three dimensional flows. PCR, PBCG and PCGS are shown to be superior to the vectorized strongly implicit procedure (SIP) proposed by Stone when they are used together with PCG.