Optimization of the Iteration Parameters of the Krylov Subspace Methods for Simulation of Incompressible Flow

In optimizing the iteration parameters of the SIMPLE-like numerical procedure, a genetic algorithm (GA) which searches for a minimum calculation time in a space of iteration numbers was developed. A methodology has been presented for the numerical solution of natural convection in a squeezed cavity at Rayleigh number of 10 and Pr number of 10.0. The pressure correction equation was employed in a conjugate gradient (CG) method with a relative incomplete factorization (RILU(0)) preconditioner. The temperature equation was solved by using preconditioned Krylov subspace methods: the generalized minimum residual (GMRES) method and the bi-conjugate gradient-stabilized (BICGSTAB) method with a RILU(0) preconditioner. The momentum equation was treated by means of the successive overrelaxation (SOR), Gauss-Seidel (GS), GMRES, and GMRES with symmetric Gauss-Seidel (SGS) preconditioner methods. We analyze computed results and we discuss how the calculation time depends on methods and on changes of iteration parameters. The calculation times were not strongly influenced by use of the RILU(0) preconditioner with optimal and close-to-optimal combinations of the perturbation and lumping coefficients, but changed sharply with changes in the pressure iteration parameter.