A finite volume unstructured multigrid method for efficient computation of unsteady incompressible viscous flows

An unstructured non-nested multigrid method is presented for efficient simulation of unsteady incompressible Navier-Stokes flows. The Navier-Stokes solver is based on the artificial compressibility approach and a higher-order characteristics-based finite-volume scheme on unstructured grids. Unsteady flow is calculated with an implicit dual time stepping scheme. For efficient computation of unsteady viscous flows over complex geometries, an unstructured multigrid method is developed to speed up the convergence rate of the dual time stepping calculation. The multigrid method is used to simulate the steady and unsteady incompressible viscous flows over a circular cylinder for validation and performance evaluation purposes. It is found that the multigrid method with three levels of grids results in a 75% reduction in CPU time for the steady flow calculation and 55% reduction for the unsteady flow calculation, compared with its single grid counterparts. The results obtained are compared with numerical solutions obtained by other researchers as well as experimental measurements wherever available and good agreements are obtained.