Variants of biconjugate gradient method for compressible Navier-Stokes solver

The variants of a biconjugate gradient method with a preconditioner of incomplete lower upper factorization are implemented for solving full Navier-Stokes equations with a κ-ε two-equation model of turbulence and for resolving the problem of slow convergence, if the widely used approximate factorization method is employed. The conjugate gradient squared biconjugate gradient stable and the transpose of free quasiminimal residual algorithm are the selected approaches to speed up the convergence rate and remove the irregular convergent behavior. The Reynolds averaged Navier-Stokes equations are discretized with an implicit total variation diminishing algorithm. The superiority of the new schemes is demonstrated by the comparisons of the convergence rate with the three variant biconjugate gradient methods and by the approximate factorization method for the computations of the turbulent, transonic, separated flow over an axisymmetric bump, and the projectile of a flat base. The results show that fast convergence rate can be achieved by the preconditioned variants of the biconjugate gradient methods, and the residuals can be further reduced as the iterations are continued. This implies that the computation of the turbulent flow with a two-equation model of turbulence can be a practical possibility in a reasonable computer time and with very good accuracy.