A computational multilevel approach for solving 2D Navier–Stokes equations over non-matching grids

A multilevel approach with parallel implementation is developed for obtaining fast solutions of the Navier–Stokes equations solved on domains with non-matching grids. The method relies on computing solutions over different subdomains with different multigrid levels by using multiple processors. A local Vanka-type relaxation operator for the multigrid solution of the Navier–Stokes system allows solutions to be computed at the element level. The natural implementation on a multiprocessor architecture results in a straightforward and flexible algorithm. Numerical computations are presented, using benchmark applications, in order to support the method. Parallelization is discussed to achieve proper accuracy, load balancing and computational efficiency between different processors.