Eulerian formulation of the interacting particle representation model of homogeneous turbulence

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

doi:10.1103/PhysRevFluids.1.064404

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

Journal Article · Fri Oct 21 00:00:00 EDT 2016 · Physical Review Fluids

DOI:https://doi.org/10.1103/PhysRevFluids.1.064404· OSTI ID:1399708

Campos, Alejandro ^[1]; Duraisamy, Karthik ^[2]; Iaccarino, Gianluca ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Michigan, Ann Arbor, MI (United States)
Stanford Univ., CA (United States)

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 the 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1399708

Report Number(s):: LLNL--JRNL-733859

Journal Information:: Physical Review Fluids, Journal Name: Physical Review Fluids Journal Issue: 6 Vol. 1; ISSN 2469-990X

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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