COMPARISON OF VARIANTS OF THE BI-CONJUGATE GRADIENT-METHOD FOR COMPRESSIBLE NAVIER-STOKES SOLVER WITH 2ND-MOMENT CLOSURE

Variants of the bi-conjugate gradient (Bi-CG) method are used to resol ve the problem of slow convergence in CFD when it is applied to comple x flow field simulation using higher-order turbulence models. In this study the Navier-Stokes and Reynolds stress transport equations are di scretized with an implicit, total variation diminishing (TVD), finite volume formulation. The preconditioning technique of incomplete lower- upper (ILU) factorization is incorporated into the conjugate gradient square (CGS), bi-conjugate gradient stable (Bi-CGSTAB) and transpose-f ree quasi-minimal residual (TFQMR) algorithms to accelerate convergenc e of the overall itertive methods. Computations have been carried out for separated flow fields over transonic bumps, supersonic bases and s upersonic compression corners. By comparisons of the convergence rate with each other and with the conventional approximate factorization (A F) method it is shown that the Bi-CGSTAB method gives the most efficie nt convergence rate among these methods and can speed up the CPU time by a factor of 2.4-6.5 as compared with the AF method. Moreover, the A F method may yield somewhat different results from variants of the Bi- CG method owing to the factorization error which introduces a higher l evel of convergence criterion.