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Title: High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks

Abstract

Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ( “High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement studymore » to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. As a result, one of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.« less

Authors:
 [1];  [2];  [2];  [3];  [4]
  1. Bay Area Environmental Research Institute, Petaluma, CA (United States)
  2. NASA-Ames Research Center, Moffett Field, CA (United States)
  3. CORIA UMR 6614 & INSA de Rouen, St-Etienne du Rouvray (France)
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1477827
Report Number(s):
LLNL-JRNL-748257
Journal ID: ISSN 1815-2406; applab; 933337
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 19; Journal Issue: 02; Journal ID: ISSN 1815-2406
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; high order numerical methods; turbulent flows with shocks; Germano SGS model; LES

Citation Formats

Kotov, D. V., Yee, H. C., Wray, A. A., Hadjadj, A., and Sjögreen, B. High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks. United States: N. p., 2016. Web. doi:10.4208/cicp.211014.040915a.
Kotov, D. V., Yee, H. C., Wray, A. A., Hadjadj, A., & Sjögreen, B. High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks. United States. doi:10.4208/cicp.211014.040915a.
Kotov, D. V., Yee, H. C., Wray, A. A., Hadjadj, A., and Sjögreen, B. Mon . "High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks". United States. doi:10.4208/cicp.211014.040915a. https://www.osti.gov/servlets/purl/1477827.
@article{osti_1477827,
title = {High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks},
author = {Kotov, D. V. and Yee, H. C. and Wray, A. A. and Hadjadj, A. and Sjögreen, B.},
abstractNote = {Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ( “High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement study to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. As a result, one of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.},
doi = {10.4208/cicp.211014.040915a},
journal = {Communications in Computational Physics},
number = 02,
volume = 19,
place = {United States},
year = {2016},
month = {2}
}

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Works referenced in this record:

Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
journal, July 1989


Development of low dissipative high order filter schemes for multiscale Navier–Stokes/MHD systems
journal, July 2007


Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers
journal, November 2012

  • Yee, Helen C.; Sjögreen, Bjorn; Hadjadj, Abdellah
  • Communications in Computational Physics, Vol. 12, Issue 5
  • DOI: 10.4208/cicp.261111.130412a

A proposed modification of the Germano subgrid‐scale closure method
journal, March 1992

  • Lilly, D. K.
  • Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 3
  • DOI: 10.1063/1.858280

Toward the large-eddy simulation of compressible turbulent flows
journal, May 1992


Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters
journal, March 1999

  • Yee, H. C.; Sandham, N. D.; Djomehri, M. J.
  • Journal of Computational Physics, Vol. 150, Issue 1
  • DOI: 10.1006/jcph.1998.6177

Large-Eddy Simulation of the Shock/Turbulence Interaction
journal, July 1999

  • Ducros, F.; Ferrand, V.; Nicoud, F.
  • Journal of Computational Physics, Vol. 152, Issue 2
  • DOI: 10.1006/jcph.1999.6238

Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations
journal, February 2011


Interaction of isotropic turbulence with shock waves: effect of shock strength
journal, June 1997


Simulation of Richtmyer–Meshkov instability by sixth-order filter methods
journal, September 2007


Summation by parts, projections, and stability. I
journal, September 1995


High-Order Fluxes for Conservative Skew-Symmetric-like Schemes in Structured Meshes: Application to Compressible Flows
journal, June 2000

  • Ducros, F.; Laporte, F.; Soulères, T.
  • Journal of Computational Physics, Vol. 161, Issue 1
  • DOI: 10.1006/jcph.2000.6492

Entropy Splitting and Numerical Dissipation
journal, July 2000

  • Yee, H. C.; Vinokur, M.; Djomehri, M. J.
  • Journal of Computational Physics, Vol. 162, Issue 1
  • DOI: 10.1006/jcph.2000.6517

Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for High Order Methods
journal, April 2004


Prediction of turbulent separation over a backward-facing smooth ramp
journal, January 2005


LES of temporally evolving mixing layers by an eighth-order filter scheme: LES OF TEMPORALLY EVOLVING MIXING LAYERS BY EIGHTH-ORDER FILTER SCHEME
journal, January 2012

  • Hadjadj, Abdellah; Yee, Helen C.; Sjögreen, Bjorn
  • International Journal for Numerical Methods in Fluids, Vol. 70, Issue 11
  • DOI: 10.1002/fld.2753

A dynamic subgrid‐scale eddy viscosity model
journal, July 1991

  • Germano, Massimo; Piomelli, Ugo; Moin, Parviz
  • Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
  • DOI: 10.1063/1.857955

Entropy Splitting for High-Order Numerical Simulation of Compressible Turbulence
journal, May 2002

  • Sandham, N. D.; Li, Q.; Yee, H. C.
  • Journal of Computational Physics, Vol. 178, Issue 2
  • DOI: 10.1006/jcph.2002.7022

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves
journal, February 2010

  • Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.
  • Journal of Computational Physics, Vol. 229, Issue 4
  • DOI: 10.1016/j.jcp.2009.10.028

A Subgrid-Scale Deconvolution Approach for Shock Capturing
journal, May 2002


ENO schemes with subcell resolution
journal, July 1989


High order finite difference methods with subcell resolution for advection equations with stiff source terms
journal, January 2012