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Research Papers: Fundamental Issues and Canonical Flows

A Validation Study of the Compressible Rayleigh–Taylor Instability Comparing the Ares and Miranda Codes

[+] Author and Article Information
Thomas J. Rehagen

Lawrence Livermore National Laboratory,
Livermore, CA 94550
e-mail: rehagen1@llnl.gov

Jeffrey A. Greenough

Lawrence Livermore National Laboratory,
Livermore, CA 94550,

Britton J. Olson

Lawrence Livermore National Laboratory,
Livermore, CA 94550

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 20, 2016; final manuscript received January 13, 2017; published online April 20, 2017. Assoc. Editor: Praveen Ramaprabhu.The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Fluids Eng 139(6), 061204 (Apr 20, 2017) (9 pages) Paper No: FE-16-1689; doi: 10.1115/1.4035944 History: Received October 20, 2016; Revised January 13, 2017

The compressible Rayleigh–Taylor (RT) instability is studied by performing a suite of large eddy simulations (LES) using the Miranda and Ares codes. A grid convergence study is carried out for each of these computational methods, and the convergence properties of integral mixing diagnostics and late-time spectra are established. A comparison between the methods is made using the data from the highest resolution simulations in order to validate the Ares hydro scheme. We find that the integral mixing measures, which capture the global properties of the RT instability, show good agreement between the two codes at this resolution. The late-time turbulent kinetic energy and mass fraction spectra roughly follow a Kolmogorov spectrum, and drop off as k approaches the Nyquist wave number of each simulation. The spectra from the highest resolution Miranda simulation follow a Kolmogorov spectrum for longer than the corresponding spectra from the Ares simulation, and have a more abrupt drop off at high wave numbers. The growth rate is determined to be between around 0.03 and 0.05 at late times; however, it has not fully converged by the end of the simulation. Finally, we study the transition from direct numerical simulation (DNS) to LES. The highest resolution simulations become LES at around t/τ ≃ 1.5. To have a fully resolved DNS through the end of our simulations, the grid spacing must be 3.6 (3.1) times finer than our highest resolution mesh when using Miranda (Ares).

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Figures

Grahic Jump Location
Fig. 2

The mixing width as a function of time computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c): (a) Miranda, (b) Ares, and (c) mesh D for Miranda and Ares

Grahic Jump Location
Fig. 3

The mixedness as a function of time computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c): (a) Miranda, (b) Ares, and (c) mesh D for Miranda and Ares

Grahic Jump Location
Fig. 5

Spectra of the turbulence kinetic energy at t/τ = 13 computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c). The thin black line above the spectra is thek–5∕3 fiducial. (a) Miranda (b) Ares, and (c) mesh D for Miranda and Ares

Grahic Jump Location
Fig. 7

The growth rate, αb as a function of time, computed from the highest resolution Miranda (solid lines) and Ares (dotted lines) simulations, using Eq. (30) (thick lines) and Eq. (31) (thin lines)

Grahic Jump Location
Fig. 8

The effective numerical viscosity as a function of the grid Reynolds number expression, similar to Fig. 15(b) from Ref. [56]. Blue symbols are data from Miranda and red are from Ares. The circle, square, triangle, and diamond values are calculated at t/τ = 0.5, 1, 1.5, and 3 respectively. See text for details.

Grahic Jump Location
Fig. 9

The time dependence of the slope of the data points in Fig. 8. The black points are calculated from the highest resolution (mesh D) data, while the red, blue, and purple points are from mesh C, mesh B, and mesh A, respectively. The dashed gray line is at a slope of −1.4.

Grahic Jump Location
Fig. 1

The initial perturbation spectrum given in Eq. (13)

Grahic Jump Location
Fig. 4

The mixed mass as a function of time computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c): (a) Miranda, (b) Ares, and (c) mesh D for Miranda and Ares

Grahic Jump Location
Fig. 10

The equilibrium density profile given in Eq. (A5) as a function of z (solid line), with the values of g, MH, ML, T0, and δ given in Sec. 2. The dashed line shows the density profile if the two fluids were not mixed across the interface initially, i.e., if there is a sharp transition between the heavy and light fluid.

Grahic Jump Location
Fig. 6

Spectra of the mass fraction of the heavier fluid at t/τ = 13 computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c). The thin black line above the spectra is the k−5∕3 fiducial.

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