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).
Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of Compressible Flow Similarity Solutions
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.
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Ramsey, S. D., Ivancic, P. R., and Lilieholm, J. F. (December 10, 2015). "Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of Compressible Flow Similarity Solutions." ASME. J. Verif. Valid. Uncert. June 2016; 1(2): 021003. https://doi.org/10.1115/1.4030929
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