Premium
A simplified two‐level subgrid stabilized method with backtracking technique for incompressible flows at high Reynolds numbers
Author(s) -
Yang Xiaocheng,
Shang Yueqiang,
Zheng Bo
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22657
Subject(s) - mathematics , discretization , finite element method , reynolds number , grid , convergence (economics) , navier–stokes equations , nonlinear system , projection method , projection (relational algebra) , compressibility , rate of convergence , mathematical optimization , mathematical analysis , algorithm , geometry , computer science , key (lock) , mechanics , dykstra's projection algorithm , physics , computer security , quantum mechanics , turbulence , economics , thermodynamics , economic growth
Based 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.