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Title: Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

Abstract

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

Authors:
 [1]; ORCiD logo [1];  [2]
+ Show Author Affiliations
  1. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Aerospace Engineering
  2. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1850304
Alternate Identifier(s):
OSTI ID: 1638091
Grant/Contract Number:  
NA0002374
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 419; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Science; Physics; B-splines; Filters; High-resolution methods; Turbulence simulations

Citation Formats

Bay, Yong Yi, Bodony, Daniel J., and Freund, Jonathan B. Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence. United States: N. p., 2020. Web. doi:10.1016/j.jcp.2020.109680.
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Bay, Yong Yi, Bodony, Daniel J., & Freund, Jonathan B. Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence. United States. https://doi.org/10.1016/j.jcp.2020.109680
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Bay, Yong Yi, Bodony, Daniel J., and Freund, Jonathan B. Thu . "Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence". United States. https://doi.org/10.1016/j.jcp.2020.109680. https://www.osti.gov/servlets/purl/1850304.
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@article{osti_1850304,
title = {Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence},
author = {Bay, Yong Yi and Bodony, Daniel J. and Freund, Jonathan B.},
abstractNote = {A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.},
doi = {10.1016/j.jcp.2020.109680},
journal = {Journal of Computational Physics},
number = C,
volume = 419,
place = {United States},
year = {Thu Jun 25 00:00:00 EDT 2020},
month = {Thu Jun 25 00:00:00 EDT 2020}
}
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Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2020.109680
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