A Nonlinear Subgrid Stabilization Parameter-Free Method to Solve Incompressible Navier-Stokes Equations at High Reynolds Numbers

Abstract

In this work we evaluate a Nonlinear Subgrid Stabilization parameter-free method to solve time-independent incompressible Navier-Stokes equations (NSGS-NS) at high Reynolds numbers, considering only the decomposition of the velocity field (not pressure) into coarse/resolved scales and fine/unresolved scales. In this formulation we use a dynamic damping factor which it is often essential for the nonlinear iterative process and for the reduction of the number of iterations. In order to reduce the computational costs typical of two-scale methods, the unresolved scale space is defined using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. Accuracy comparisons with the streamline-upwind/Petrov-Galerkin (SUPG) formulation combined with the pressure stabilizing/Petrov-Galerkin (PSPG) are conducted based on 2D steady state benchmark problems with high Reynolds numbers, flow over a backward-facing step and lid-driven square cavity flow.