Comparison of different agglomeration multigrid schemes for compressible and incompressible flow simulations

Different parallel agglomeration multigrid schemes have been developed aiming to improve the computational performance of a compressible and an incompressible academic Computational Fluid Dynamics (CFD) codes, named Galatea and Galatea-I, respectively. Flow prediction is succeeded via the implementation of Reynolds-Averaged Navier-Stokes (RANS) equations combined with appropriate turbulence models on three-dimensional unstructured tetrahedral or hybrid meshes. The sequence of required coarser grids, composed of irregular polyhedral elements, is generated either with the isotropic or directional (full- or semi-coarsening) fusion of neighbouring control volumes on a topology-preserving framework; it resembles the advancing-front technique as it begins from solid wall surfaces and extends successively to the interior domain. The multigrid accelerated approximation of flow and turbulence equations is achieved via the V-cycle implementation of either the Full Approximation Scheme (FAS) or its coupled version with Full Multigrid (FMG) method. Multigrid approaches with different agglomeration and solution strategies have been extensively tested against three- and quasi-three-dimensional test cases, all of them demonstrating their potential for considerably improved efficiency. Their contributions to the reduction of simulations' computation time are analysed, while additionally the differences due to the type of the flow (compressible or incompressible) are thoroughly discussed.