This work is concerned with the use of Guderley's converging shock wave solution of the inviscid compressible flow equations as a verification test problem for compressible flow simulation software. In practice, this effort is complicated by both the semi-analytical nature and infinite spatial/temporal extent of this solution. 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, scale-invariant 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 scale-invariant shock wave propagation as a piston-driven flow in the context of the Guderley problem, which features a semi-analytical solution of infinite spatial/temporal extent. The semi-analytical solution allows for the derivation of a similarly semi-analytical piston boundary condition (BC) for use in Lagrangian compressible flow solvers. The consequences of utilizing this BC (as opposed to directly initializing the Guderley solution in a computational spatial grid at a fixed time) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors, global convergence rates). For the examples considered in this work, the piston-driven initialization approach is demonstrated to be a viable alternative to the more traditional, direct initialization approach.
Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of the Guderley Problem
Manuscript received March 30, 2017; final manuscript received September 5, 2017; published online September 26, 2017. Assoc. Editor: Jeffrey E. Bischoff.
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., and Lilieholm, J. F. (September 26, 2017). "Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of the Guderley Problem." ASME. J. Verif. Valid. Uncert. September 2017; 2(3): 031001. https://doi.org/10.1115/1.4037888
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