Effects of resolution inhomogeneity in large-eddy simulation

Gopal R. Yalla, Todd A. Oliver, Sigfried W. Haering, Björn Engquist, and Robert D. Moser
Phys. Rev. Fluids 6, 074604 – Published 8 July 2021

Abstract

Large-eddy simulation (LES) of turbulence in complex geometries is often conducted using strongly inhomogeneous resolution. The issues associated with resolution inhomogeneity are related to the noncommutativity of the filtering and differentiation operators, which introduces a commutation term into the governing equations. Neglect of this commutation term gives rise to commutation error. While the commutation error is well recognized, it is often ignored in practice. Moreover, the commutation error arising from the implicit part of the filter (i.e., projection onto the underlying discretization) has not been well investigated. Modeling the commutator between numerical projection and differentiation is crucial for correcting errors induced by resolution inhomogeneity in practical LES settings, which typically rely solely on implicit filtering. Here we employ a multiscale asymptotic analysis to investigate the characteristics of the commutator. This provides a statistical description of the commutator, which can serve as a target for the statistical characteristics of a commutator model. Further, we investigate how commutation error manifests in simulation and demonstrate its impact on the convection of a packet of homogeneous isotropic turbulence through an inhomogeneous grid. A connection is made between the commutation error and the propagation properties of the underlying numerics. A modeling approach for the commutator is proposed that is applicable to LES with filters that include projections to the discrete solution space and that respects the numerical properties of the LES evolution equation. It may also be useful in addressing other LES modeling issues such as discretization error.

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  • Received 9 October 2020
  • Accepted 23 June 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.074604

©2021 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

Gopal R. Yalla1, Todd A. Oliver1, Sigfried W. Haering1,2, Björn Engquist1,3, and Robert D. Moser1,4

  • 1Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
  • 2Sandia National Laboratories, Livermore, California 94551, USA
  • 3Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA
  • 4Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA

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Issue

Vol. 6, Iss. 7 — July 2021

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