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Assessment of subgrid-scale models for the incompressible Navier–Stokes equations

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
234
Issue
2
Identifiers
DOI: 10.1016/j.cam.2009.12.051
Keywords
  • Navier–Stokes Equations
  • Subgrid Model
  • Eddy Viscosity
  • Pressure Stabilization Method
  • Error Analysis
  • Numerical Tests

Abstract

Abstract In this paper, we assess two kinds of subgrid finite element methods for the two-dimensional (2D) incompressible Naver-Stokes equations (NSEs). These methods introduce subgrid-scale (SGS) eddy viscosity terms which do not act on the large flow structures. The eddy viscous terms consist of the fluid flow fluctuation strain rate stress tensors. The fluctuation tensor can be calculated by a elliptic projection or a simple L 2 projection (projective filter) in finite element spaces. The finite element pair P 2 / P 1 is adopted to numerically implement analysis and computation. We give a complete error analysis based on the assumptions of some regularity conditions. On the part of numerical tests, the numerical computations for the stationary flows show that the numerical results agree with some benchmark solutions and theoretical analysis very well. Furthermore, the given SGS models are applied to the non-stationary fluid flows.

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