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Title: Eulerian formulation of the interacting particle representation model of homogeneous turbulence

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an Eulerian framework and evolution equations are developed for the marginal PDFs. Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. A specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and themore » shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Michigan, Ann Arbor, MI (United States)
  3. Stanford Univ., CA (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-733859
Journal ID: ISSN 2469-990X; TRN: US1703089
Grant/Contract Number:
AC52-07NA27344
Type:
Accepted Manuscript
Journal Name:
Physical Review Fluids
Additional Journal Information:
Journal Volume: 1; Journal Issue: 6; Journal ID: ISSN 2469-990X
Publisher:
American Physical Society (APS)
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1399708