A simplified two‐level subgrid stabilized method with backtracking technique for incompressible flows at high Reynolds numbers

Abstract

AbstractBased on finite element discretization, a simplified two‐level subgrid stabilized method with backtracking technique is proposed for the steady incompressible Navier–Stokes equations at high Reynolds numbers. The method combines the best algorithmic characteristics of the standard two‐level method with backtracking technique and subgrid stabilized method. In this method, we first solve a fully nonlinear Navier–Stokes equations with a subgrid stabilized term on a coarse grid, then solve a simplified subgrid stabilized linear problem on a fine grid, and finally solve a linear correction problem on a coarse grid, where the stabilized term is based on an elliptic projection. The theoretical results show that, with suitable scalings of algorithmic parameters, the method can yield an optimal convergence rate of second‐order. Two numerical results are given to demonstrate the effectiveness of the method.