A multigrid method with higher-order discretization schemes

The implementation of the multigrid method into the SIMPLE algorithm presents interesting aspects concerning the mass fluxes conservation on coarser grids, the k-epsilon turbulence model and the higher-order discretization schemes. Higher-order discretization schemes for the convection terms are increasingly used in order to guarantee accuracy in demanding engineering applications. However, when used in single-grid algorithms, their convergence is considerably slower compared with the first-order schemes. Unbounded higher-order schemes offer maximum accuracy, but quite often they do not converge due to their oscillatory behaviour. This paper demonstrates the dual function of the multigrid method: reduction of CPU time and stabilization of the iterating procedure, making it possible to perform computations with the third-order accurate QUICK scheme in all cases. The method is applied to the calculation of two- and three-dimensional flows with or without turbulence modelling. The results show that the convergence rate of the present algorithm does not deteriorate when QUICK is used and that, if applied on complex engineering cases, large gains in computational time can be achieved. Copyright (C) 2001 John Wiley & Sons, Ltd.