Multigrid acceleration for recirculating laminar and turbulent flows computed with a non-orthogonal, collocated finite-volume scheme Original Research Article

A study has been undertaken of multigrid convergence acceleration in iterative calculations of recirculating laminar and turbulent flows. The basic numerical platform is a 2D/3D non-orthogonal, collocated finite-volume algorithm in which convection is approximated, optionally, by a non-monotonic upstream-weighted third-order scheme or by a monotonie second-order MUSCL/TVD formulation, and which iterates the solution towards the steady state by way of a pressure-correction scheme. The study investigates the performance of various multigrid implementations including the correction and full approximation multigrid variants, the latter operated within a variety of cycles, both with prescribed and residual-driven relaxation sweeps at each grid level. The multigrid implementation is documented in detail and includes a consideration of data-structure issues and special algorithmic measures necessary to secure robust convergence for turbulent flows. The performance characteristics of the multigrid variants are then exposed through a range of results arising from computations for laminar and turbulent conditions, with turbulence being represented by the k-ϵ model or full Reynolds-stress-transport closure.