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Research Papers

Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of Compressible Flow Similarity Solutions

[+] Author and Article Information
Scott D. Ramsey

Mem. ASME
Los Alamos National Laboratory,
P.O. Box 1663, MS T082,
Los Alamos, NM 87545
e-mail: ramsey@lanl.gov

Philip R. Ivancic

Department of Aerospace Engineering,
Mississippi State University,
330 Walker Engineering Laboratory,
Mississippi State, MS 39762
e-mail: pri4@msstate.edu

Jennifer F. Lilieholm

Department of Physics and Astronomy,
University of Maine,
2 Bennett Hall,
Orono, ME 04469
e-mail: Jennifer.Lilieholm@maine.edu

1Corresponding author.

Manuscript received January 12, 2015; final manuscript received May 20, 2015; published online December 10, 2015. Assoc. Editor: William Rider.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 1(2), 021003 (Dec 10, 2015) (10 pages) Paper No: VVUQ-15-1002; doi: 10.1115/1.4030929 History: Received January 12, 2015; Revised May 20, 2015

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston” is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. The consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).

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Figures

Grahic Jump Location
Fig. 1

Direct initialization of a similarity solution onto a computational spatial grid

Grahic Jump Location
Fig. 2

Piston initialization of a similarity solution onto a computational spatial grid

Grahic Jump Location
Fig. 3

One-dimensional planar Zel'dovich problem density simulation results for direct (left) and piston (right) initialization methods

Grahic Jump Location
Fig. 4

Two-dimensional planar modified Cog19 problem density simulation results for direct (left) and piston (right) initialization methods

Grahic Jump Location
Fig. 5

One-dimensional spherical Cog20 problem density simulation results for direct (left) and piston (right) initialization methods

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