Robust verification analysis

JOURNAL OF COMPUTATIONAL PHYSICS

卷:307

Article

Rider, William¹  Witkowski, Walt²  Kamm, James R.³  Wildey, Tim¹ 

[1] Sandia Natl Labs, Ctr Res Comp, POB 5800, Albuquerque, NM 87185 USA

[2] Sandia Natl Labs, Engn Sci Ctr, Credibil Proc Dept, Verificat & Validat,Uncertainty Quantificat, POB 5800, Albuquerque, NM 87185 USA

[3] Los Alamos Natl Lab, Methods & Algorithms Grp, Computat Phys Div, POB 1663, Los Alamos, NM 87545 USA

关键词: Verification;    Error estimate;    Convergence;    Order-of-accuracy;    Solution verification;    Robust statistics;   

DOI  :  10.1016/j.jcp.2015.11.054

来源: Elsevier

【 摘 要 】

We introduce a new methodology for inferring the accuracy of computational simulations through the practice of solution verification. We demonstrate this methodology on examples from computational heat transfer, fluid dynamics and radiation transport. Our methodology is suited to both well-and ill-behaved sequences of simulations. Our approach to the analysis of these sequences of simulations incorporates expert judgment into the process directly via a flexible optimization framework, and the application of robust statistics. The expert judgment is systematically applied as constraints to the analysis, and together with the robust statistics guards against over-emphasis on anomalous analysis results. We have named our methodology Robust Verification. Our methodology is based on utilizing multiple constrained optimization problems to solve the verification model in a manner that varies the analysis' underlying assumptions. Constraints applied in the analysis can include expert judgment regarding convergence rates (bounds and expectations) as well as bounding values for physical quantities (e.g., positivity of energy or density). This approach then produces a number of error models, which are then analyzed through robust statistical techniques (median instead of mean statistics). This provides self-contained, data and expert informed error estimation including uncertainties for both the solution itself and order of convergence. Our method produces high quality results for the well-behaved cases relatively consistent with existing practice. The methodology can also produce reliable results for ill-behaved circumstances predicated on appropriate expert judgment. We demonstrate the method and compare the results with standard approaches used for both code and solution verification on well-behaved and ill-behaved simulations. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free