Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of the Guderley Problem

[+] Author and Article Information
Scott D. Ramsey

Member, ASME, Applied Physics, Los Alamos National Laboratory, PO Box 1663, MS T082, Los Alamos, NM 87545

Jennifer Lilieholm

Department of Physics, University of Washington, 3910 15th Ave NE, Seattle, WA 98195

1Corresponding author.

ASME doi:10.1115/1.4037888 History: Received March 30, 2017; Revised September 05, 2017


This work is concerned with the use of Guderley converging shock wave solution of the inviscid compressible flow equations as a benchmark or verification test problem for finite volume 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 for use in Lagrangian compressible flow solvers. The consequences of utilizing this boundary condition (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).

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