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Research Papers

Verification Studies for the Noh Problem Using Nonideal Equations of State and Finite Strength Shocks

[+] Author and Article Information
Sarah C. Burnett

Department of Mathematics,
University of Maryland, College Park
College Park, MD 20742
e-mail: burnetts@math.umd.edu

Kevin G. Honnell

Computational Physics Division,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: kgh@lanl.gov

Scott D. Ramsey

Theoretical Design Division,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: ramsey@lanl.gov

Robert L. Singleton, Jr.

Computational Physics Division,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: bobs1@lanl.gov

Manuscript received June 16, 2017; final manuscript received July 21, 2018; published online September 17, 2018. Assoc. Editor: Sumanta Acharya. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, 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. Verif. Valid. Uncert 3(2), 021002 (Sep 17, 2018) (10 pages) Paper No: VVUQ-17-1023; doi: 10.1115/1.4041195 History: Received June 16, 2017; Revised July 21, 2018

The Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan–Starling EOS for hard-sphere fluids. Self-similarity methods are used to solve the Euler compressible flow equations, which, in combination with the Rankine–Hugoniot jump conditions, provide a tractable general solution. This solution can be applied to fluids with EOSs that meet criterion such as it being a convex function and having a corresponding bulk modulus. For the planar case, the solution can be applied to shocks of arbitrary strength, but for the cylindrical and spherical geometries, it is required that the analysis be restricted to strong shocks. The exact solutions are used to perform a variety of quantitative code verification studies of the Los Alamos National Laboratory Lagrangian hydrocode free Lagrangian (FLAG).

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Figures

Grahic Jump Location
Fig. 1

The planar one-dimensional Noh problem (t = 0)—a uniform inwardly flowing fluid with pressure p0 and density ρ0 impinges on a hard wall (or an axis or a point in the cylindrical or spherical geometries)

Grahic Jump Location
Fig. 2

The planar one-dimensional Noh problem (t > 0)—an outwardly moving shock wave with a stagnant, compressed fluid behind it

Grahic Jump Location
Fig. 3

Convergence study for the planar Noble-Abel case when p0 = 1 Mbar and b = 0.4 cm3/g

Grahic Jump Location
Fig. 4

Density plots of the planar Noble-Abel gas, γ = 5/3, ρ0 = 1.0 g/cm3, b = 0.1 cm3/g: (a) p0 = 0.00 Mbar, (b) p0 = 0.01 Mbar, (c) p0 = 0.10 Mbar, and (d) p0 = 1.00 Mbar

Grahic Jump Location
Fig. 5

Density plots of the planar Noble-Abel gas, γ = 5/3, ρ0 = 1.0 g/cm3, p0 = 0.0 Mbar: (a) b = −0.2 cm3/g, (b) b = 0.0 cm3/g, (c) b = 0.2 cm3/g, (d) b = 0.4 cm3/g

Grahic Jump Location
Fig. 6

Density plots of the spherical Noble-Abel gas, γ = 5/3, ρ0 = 1.0 g/cm3, p0 = 0.0 Mbar: (a) b = 0.00 cm3/g, (b) b = 0.01 cm3/g, (c) b = 0.10 cm3/g, and (d) b = 0.20 cm3/g

Grahic Jump Location
Fig. 7

Relative error plots of the spherical Noble-Abel gas, γ = 5/3, ρ0 = 1.0 g/cm3, p0 = 0.0 Mbar: (a) b = 0.00 cm3/g, (b) b = 0.01 cm3/g, (c) b = 0.10 cm3/g, and (d) b = 0.20 cm3/g

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