Convergence acceleration of segregated algorithms using dynamic tuning additive correction multigrid strategy

A convergence acceleration method based on an additive correction multigrid-SIMPLEC (ACM-S) algorithm with dynamic tuning of the relaxation factors is presented. In the ACM-S method, the coarse grid velocity correction components obtained from the mass conservation (velocity potential) correction equation are included into the fine grid momentum equations before the coarse grid momentum correction equations are formed using the additive correction methodology. Therefore, the coupling between the momentum and mass conservation equations is obtained on the coarse grid, while maintaining the segregated structure of the single grid algorithm. This allows the use of the same solver (smoother) on the coarse grid. For turbulent flows with heat transfer, additional scalar equations are solved outside of the momentum-mass conservation equations loop. The convergence of the additional scalar equations is accelerated using a dynamic tuning of the relaxation factors. Both a relative error (RE) scheme and a local Reynolds/Peclet (ER/P) relaxation scheme methods are used. These methodologies are tested for laminar isothermal flows and turbulent flows with heat transfer over geometrically complex two- and three-dimensional configurations. Savings up to 57% in CPU time are obtained for complex geometric domains representative of practical engineering problems.