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Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers. (English) Zbl 1121.76036
Summary: A subgrid stabilization technique is developed for solving 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 viscous incompressible flows around the airfoil NACA0012 at zero incidence and Reynolds numbers ranging from ${10}^{5}$ to ${10}^{6}$.
##### MSC:
 76M10 Finite element methods (fluid mechanics) 76D05 Navier-Stokes equations (fluid dynamics)