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research-article

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
ramsey@lanl.gov

Jennifer Lilieholm

Department of Physics, University of Washington, 3910 15th Ave NE, Seattle, WA 98195
liliej@uw.edu

1Corresponding author.

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

Abstract

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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