skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Effects of operator splitting and low Mach-number correction in turbulent mixing transition simulations

Abstract

In this paper, transition and turbulence decay with the Taylor–Green vortex have been effectively used to demonstrate emulation of high Reynolds-number ( R e ) physical dissipation through numerical convective effects of various non-oscillatory finite-volume algorithms for implicit large eddy simulation (ILES), e.g. using the Godunov-based Eulerian adaptive mesh refinement code xRAGE. The inverse-chevron shock tube experiment simulations have been also used to assess xRAGE based ILES for shock driven turbulent mixing, compared with available simulation and laboratory data. The previous assessments are extended to evaluate new directionally-unsplit high-order algorithms in xRAGE, including a correction to address the well-known issue of excessive numerical diffusion of shock-capturing (e.g., Godunov-type) schemes for low Mach numbers. The unsplit options for hydrodynamics in xRAGE are discussed in detail, followed by fundamental tests with representative shock problems. Basic issues of transition to turbulence and turbulent mixing are discussed, and results of simulations of high- R e turbulent flow and mixing in canonical test cases are reported. Finally, compared to the directional-split cases, and for each grid resolution considered, unsplit results exhibit transition to turbulence with much higher effective R e —and significantly more so with the low Mach number correction.

Authors:
ORCiD logo [1];  [1];  [1];  [1];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1441319
Report Number(s):
LA-UR-17-31238
Journal ID: ISSN 0898-1221
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 78; Journal Issue: 2; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; shock-driven turbulence; material mixing; Eulerian methods

Citation Formats

Grinstein, F. F., Saenz, J. A., Dolence, J. C., Masser, T. O., Rauenzahn, R. M., and Francois, M. M.. Effects of operator splitting and low Mach-number correction in turbulent mixing transition simulations. United States: N. p., 2018. Web. https://doi.org/10.1016/j.camwa.2018.05.008.
Grinstein, F. F., Saenz, J. A., Dolence, J. C., Masser, T. O., Rauenzahn, R. M., & Francois, M. M.. Effects of operator splitting and low Mach-number correction in turbulent mixing transition simulations. United States. https://doi.org/10.1016/j.camwa.2018.05.008
Grinstein, F. F., Saenz, J. A., Dolence, J. C., Masser, T. O., Rauenzahn, R. M., and Francois, M. M.. Thu . "Effects of operator splitting and low Mach-number correction in turbulent mixing transition simulations". United States. https://doi.org/10.1016/j.camwa.2018.05.008. https://www.osti.gov/servlets/purl/1441319.
@article{osti_1441319,
title = {Effects of operator splitting and low Mach-number correction in turbulent mixing transition simulations},
author = {Grinstein, F. F. and Saenz, J. A. and Dolence, J. C. and Masser, T. O. and Rauenzahn, R. M. and Francois, M. M.},
abstractNote = {In this paper, transition and turbulence decay with the Taylor–Green vortex have been effectively used to demonstrate emulation of high Reynolds-number (Re) physical dissipation through numerical convective effects of various non-oscillatory finite-volume algorithms for implicit large eddy simulation (ILES), e.g. using the Godunov-based Eulerian adaptive mesh refinement code xRAGE. The inverse-chevron shock tube experiment simulations have been also used to assess xRAGE based ILES for shock driven turbulent mixing, compared with available simulation and laboratory data. The previous assessments are extended to evaluate new directionally-unsplit high-order algorithms in xRAGE, including a correction to address the well-known issue of excessive numerical diffusion of shock-capturing (e.g., Godunov-type) schemes for low Mach numbers. The unsplit options for hydrodynamics in xRAGE are discussed in detail, followed by fundamental tests with representative shock problems. Basic issues of transition to turbulence and turbulent mixing are discussed, and results of simulations of high-Re turbulent flow and mixing in canonical test cases are reported. Finally, compared to the directional-split cases, and for each grid resolution considered, unsplit results exhibit transition to turbulence with much higher effective Re—and significantly more so with the low Mach number correction.},
doi = {10.1016/j.camwa.2018.05.008},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 2,
volume = 78,
place = {United States},
year = {2018},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Slices of density at time t = 0.026 on the x = 0, y = 0 and z = 0 planes on the first (positive) octant, from the 3d Sedov spherical blast wave simulations using the default split hydro scheme (a, c), and the unsplit hydro scheme (b,more » d), on a cartesian mesh with 5 level AMR ($Δx$ = 1/512) and 6 level AMR (1/1024), respectively. All quantities are non-dimensional.« less

Save / Share:

Works referenced in this record:

On integrating large eddy simulation and laboratory turbulent flow experiments
journal, July 2009

  • Grinstein, Fernando F.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 367, Issue 1899
  • DOI: 10.1098/rsta.2009.0059

An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence
journal, April 1996


On the computation of instabilities and symmetry-breaking in fluid mechanics
journal, November 2005


The RAGE radiation-hydrodynamic code
journal, October 2008


Glimm’s Method for Gas Dynamics
journal, March 1982

  • Colella, Phillip
  • SIAM Journal on Scientific and Statistical Computing, Vol. 3, Issue 1
  • DOI: 10.1137/0903007

Towards the Ultimate Conservative Difference Scheme
journal, August 1997


Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
journal, March 2011

  • Grinstein, F. F.; Gowardhan, A. A.; Wachtor, A. J.
  • Physics of Fluids, Vol. 23, Issue 3
  • DOI: 10.1063/1.3555635

Three-dimensional simulation strategy to determine the effects of turbulent mixing on inertial-confinement-fusion capsule performance
journal, May 2014


Efficient implementation of essentially non-oscillatory shock-capturing schemes
journal, August 1988


An improved reconstruction method for compressible flows with low Mach number features
journal, May 2008

  • Thornber, B.; Mosedale, A.; Drikakis, D.
  • Journal of Computational Physics, Vol. 227, Issue 10
  • DOI: 10.1016/j.jcp.2008.01.036

On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes
journal, May 2004


Turbulent mixing in spherical implosions
journal, January 2008

  • Youngs, David L.; Williams, Robin J. R.
  • International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8
  • DOI: 10.1002/fld.1594

Reynolds-averaged Navier–Stokes initialization and benchmarking in shock-driven turbulent mixing
journal, February 2013


Effects of initial condition spectral content on shock-driven turbulent mixing
journal, July 2015


Small-scale structure of the Taylor–Green vortex
journal, May 1983

  • Brachet, Marc E.; Meiron, Daniel I.; Orszag, Steven A.
  • Journal of Fluid Mechanics, Vol. 130, Issue -1
  • DOI: 10.1017/S0022112083001159

Simulation of transition and turbulence decay in the Taylor–Green vortex
journal, January 2007


Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow
journal, April 2011

  • Hahn, M.; Drikakis, D.; Youngs, D. L.
  • Physics of Fluids, Vol. 23, Issue 4
  • DOI: 10.1063/1.3576187

Estimating the effective Reynolds number in implicit large-eddy simulation
journal, January 2014


A Comparison of Three Approaches to Compute the Effective Reynolds Number of the Implicit Large-Eddy Simulations
journal, April 2016

  • Zhou, Ye; Thornber, Ben
  • Journal of Fluids Engineering, Vol. 138, Issue 7
  • DOI: 10.1115/1.4032532

A High-Order Godunov Method for Multiple Condensed Phases
journal, October 1996

  • Miller, Gregory Hale; Puckett, Elbridge Gerry
  • Journal of Computational Physics, Vol. 128, Issue 1
  • DOI: 10.1006/jcph.1996.0200

A comparative study of multimaterial Lagrangian and Eulerian methods with pressure relaxation
journal, August 2013


On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
journal, January 1983

  • Harten, Amiram; Lax, Peter D.; Leer, Bram van
  • SIAM Review, Vol. 25, Issue 1
  • DOI: 10.1137/1025002

On Godunov-Type Methods for Gas Dynamics
journal, April 1988

  • Einfeldt, Bernd
  • SIAM Journal on Numerical Analysis, Vol. 25, Issue 2
  • DOI: 10.1137/0725021

Restoration of the contact surface in the HLL-Riemann solver
journal, July 1994

  • Toro, E. F.; Spruce, M.; Speares, W.
  • Shock Waves, Vol. 4, Issue 1
  • DOI: 10.1007/BF01414629

A simple unsplit Godunov method for multidimensional MHD
journal, February 2009


Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows
journal, September 2005


The mixing transition in turbulent flows
journal, April 2000


Local isotropy in turbulent boundary layers at high Reynolds number
journal, June 1994


Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box
journal, February 2003

  • Kaneda, Yukio; Ishihara, Takashi; Yokokawa, Mitsuo
  • Physics of Fluids, Vol. 15, Issue 2
  • DOI: 10.1063/1.1539855

Dissipation in Turbulent Flows
journal, January 2015


Direct simulation of three-dimensional turbulence in the Taylor–Green vortex
journal, October 1991


Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor–Green Vortex Flow
journal, July 2005

  • Shu, Chi-Wang; Don, Wai-Sun; Gottlieb, David
  • Journal of Scientific Computing, Vol. 24, Issue 1
  • DOI: 10.1007/s10915-004-5407-y

On the identification of a vortex
journal, February 1995


Observation of mix in a compressible plasma in a convergent cylindrical geometry
journal, November 2002

  • Barnes, Cris W.; Batha, S. H.; Dunne, A. M.
  • Physics of Plasmas, Vol. 9, Issue 11
  • DOI: 10.1063/1.1511730

Monotonically Integrated Large Eddy Simulation of Free Shear Flows
journal, May 1999

  • Fureby, C.; Grinstein, F. F.
  • AIAA Journal, Vol. 37, Issue 5
  • DOI: 10.2514/2.772

Implicit large-eddy simulation of passive scalar mixing in statistically stationary isotropic turbulence
journal, February 2013

  • Wachtor, A. J.; Grinstein, F. F.; DeVore, C. R.
  • Physics of Fluids, Vol. 25, Issue 2
  • DOI: 10.1063/1.4783924

    Works referencing / citing this record:

    Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities
    journal, August 2019

    • Zhou, Ye; Clark, Timothy T.; Clark, Daniel S.
    • Physics of Plasmas, Vol. 26, Issue 8
    • DOI: 10.1063/1.5088745