Subgrid Stabilized Projection Method for 2D Unsteady Flows at High Reynolds Numbers

A subgrid stabilization technique is developed for solving the two-dimensional incompressible Navier–Stokes equations at high Reynolds numbers. The time marching algorithm is based on a well-established fractional-step pressure-correction projection method. The advection–diffusion step is enriched by an implicit subgrid stabilizing term and by an explicit dissipative shock capturing term. The former is calculated by means of a hierarchical finite element setting, the latter is included to avoid Gibbs’ phenomenon in the boundary layer. Convergence tests on prototypical two-dimensional examples are reported and the method is used to simulate the viscous incompressible flows around the airfoil NACA0012 at zero incidence and Reynolds numbers ranging from 105 to 106.