Finite element error analysis of a zeroth order approximate deconvolution model based on a mixed formulation


Carolina Cardoso M., KAYA MERDAN S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.331, no.1, pp.669-685, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 331 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jmaa.2006.08.083
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.669-685
  • Keywords: zeroth order model, deconvolution, approximate deconvolution models, large eddy simulation, LARGE-EDDY SIMULATION

Abstract

A suitable discretization for the Zeroth Order Model in Large Eddy Simulation of turbulent flows is sought. This is a low order model, but its importance lies in the insight that it provides for the analysis of the higher order models actually used in practice by the pioneers Stolz and Adams [N.A. Adams, S. Stolz, On the approximate deconvolution procedure for LES, Phys. Fluids 2 (1999) 1699-1701; N.A. Adams, S. Stolz, Deconvolution methods for subgrid-scale approximation in large eddy simulation, in: B.J. Geurts (Ed.), Modem Simul. Strategies for Turbulent Flow, Edwards, Philadelphia, 2001, pp. 21-44] and others. The higher order models have proven to be of high accuracy. However, stable discretizations of them have proven to be tricky and other stabilizations, such as time relaxation and eddy viscosity, are often added. We propose a discretization based on a mixed variational formulation that gives the correct energy balance. We show it to be unconditionally stable and prove convergence. (C) 2006 Elsevier Inc. All rights reserved.