Analysis of Model Variance for Ensemble Based Turbulence Modeling

Jiang N., Kaya S., Layton W.

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, vol.15, no.2, pp.173-188, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1515/cmam-2014-0029
  • Journal Name: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.173-188
  • Keywords: Ensemble, Leray Regularization, Eddy Viscosity, Turbulence Modeling, LINEAR-SYSTEMS, ALGORITHM
  • Middle East Technical University Affiliated: Yes

Abstract

This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity co-efficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as t -> infinity; the model's variance converges to zero as t -> infinity. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effiective averaged Lyapunov exponents.