Keywords: incompressible flow, RANS, three-dimensional hybrid unstructured grids, multigrid, isotropic-directional agglomeration, parallelization.

Unstructured grids have gained a significant popularity during the past years, mainly as a result of their capability to describe accurately complex geometries with the minimum user interaction for their generation; nevertheless, the corresponding solvers are relatively inefficient compared with the structured ones. A remedy for this shortcoming appears to be the multigrid methodology, based on the solution of the flow problem on successively coarser grids. In this paper the development of a parallel agglomeration multigrid scheme is reported, enhancing an also recently developed academic computational fluid dynamics code, named Galatea-I, which employs the Reynolds-averaged Navier-Stokes equations along with the shear stress transport turbulence model, to simulate incompressible fluid flows. The fusion strategy considers either isotropic or directional adjacent control cells' merging on a topology-preserving framework, resembling the advancing front technique. The multigrid accelerated iterative solution of the flow and turbulence models is succeeded by implementing the full approximation scheme using a V-cycle strategy, incorporated though in the full multigrid scheme. The proposed algorithm is validated against benchmark test cases, concerning inviscid and turbulent incompressible flow over a rectangular wing with the NACA0012 airfoil, and three-dimensional lid driven cubic cavity laminar flow, revealing its potential for improved computational performance.

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