Abstract
This study focuses on the explicit multigrid solutions of steady and unsteady incompressible flows. An artificial compressibility based solver is adopted to couple the pressure and velocity in governing equations. This solver is validated for two and three-dimensional steady flows on staggered as well as on the collocated grids. The staggered-grid version employs a central-differencing based discretization while the explicit MacCormack scheme is used on the collocated grids. Lid-driven cavity flow is used as a test case for the steady Navier-Stokes equations while decaying Taylor-Green vortex and oscillating lid-driven cavity flow comprises the test cases for unsteady flows. A dual-time stepping within every physical time-step is used for time-accurate results for unsteady test cases. One of the primary aims of the present work is to accelerate the numerical convergence of this pseudo-compressibility based solver using multigrid methods. Therefore, a non-linear multigrid method, usually called as the full approximation storage (FAS) scheme is implemented on a grid-hierarchy. Multigrid solutions are obtained using up to four grid levels. Accelerations of up to 217 times and 70 times are reported for two and three-dimensional test cases respectively. It has been observed that these accelerations increase with the grid size; however, decrease with the increase in Reynolds number and are parameter dependent.