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J. Verif. Valid. Uncert. 2017;2(3):031001-031001-14. doi:10.1115/1.4037888.

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.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2017;2(3):031002-031002-14. doi:10.1115/1.4037887.

Validation assesses the accuracy of a mathematical model by comparing simulation results to experimentally measured quantities of interest. Model validation experiments emphasize obtaining detailed information on all input data needed by the mathematical model, in addition to measuring the system response quantities (SRQs) so that the predictive accuracy of the model can be critically determined. This article proposes a framework for assessing model validation experiments for computational fluid dynamics (CFD) regarding information content, data completeness, and uncertainty quantification (UQ). This framework combines two previously published concepts: the strong-sense model validation experiments and the modeling maturity assessment procedure referred to as the predictive capability maturity method (PCMM). The model validation experiment assessment requirements are captured in a table of six attributes: experimental facility, analog instrumentation and signal processing, boundary and initial conditions, fluid and material properties, test conditions, and measurement of system responses, with four levels of information completeness for each attribute. The specifics of this table are constructed for a generic wind tunnel experiment. Each attribute’s completeness is measured from the perspective of the level of detail needed for input data using direct numerical simulation of the Navier–Stokes equations. While this is an extraordinary and unprecedented requirement for level of detail in a model validation experiment, it is appropriate for critical assessment of modern CFD simulations.

Commentary by Dr. Valentin Fuster

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