The purpose of this project has been to provide sensitivities of results from an Eulerian hydrodynamics computer code (hydrocode) for use in design-optimization and uncertainty analyses. We began by applying an equation-based sensitivity technique used successfully in the early eighties that was applied to reactor-safety thermal-hydraulics problems, which is called Differential Sensitivity Theory (DST). The methodology is as follows: the system of partial differential equations (the forward or physical PDEs) is assembled, and differentiated with respect to the model parameters of interest; the adjoint equations are then determined using the inner-product rules of Hilbert spaces; and finally, the resulting adjoint …
continued below
Publisher Info:
Los Alamos National Lab., NM (United States)
Place of Publication:
New Mexico
Provided By
UNT Libraries Government Documents Department
Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.
Descriptive information to help identify this article.
Follow the links below to find similar items on the Digital Library.
Description
The purpose of this project has been to provide sensitivities of results from an Eulerian hydrodynamics computer code (hydrocode) for use in design-optimization and uncertainty analyses. We began by applying an equation-based sensitivity technique used successfully in the early eighties that was applied to reactor-safety thermal-hydraulics problems, which is called Differential Sensitivity Theory (DST). The methodology is as follows: the system of partial differential equations (the forward or physical PDEs) is assembled, and differentiated with respect to the model parameters of interest; the adjoint equations are then determined using the inner-product rules of Hilbert spaces; and finally, the resulting adjoint PDEs are solved using straightforward numerical operators. The forward-variable solutions when needed for the adjoint solutions are provided by the original computer code that solves the physical (or forward) problem. In the present hydrocode application, acceptable results were obtained for one-material, one-dimensional problems. The DST results were then improved by means of ''compatible'' finite difference operators. We have seen, however, that DST techniques do not produce accurate values for sensitivities to all of the parameters of interest and for problems with discontinuities such as a multi-material problem. To obtain accurate sensitivities for arbitrary numerical resolution a more code-based approach was then tried. We attempted to apply automatic differentiation (AD) in the forward mode using Automatic Differentiation of Fortran (ADIFOR, version 2.0) and the Tangent-linear and Adjoint Model Compiler (TAMC) in the forward and adjoint modes. We were successful for one-dimensional problems in both modes but failed to obtain accurate sensitivities in the adjoint mode for two-dimensional problem. Here we present the successful results for two-dimensional problems in both the forward and adjoint modes using ADIFOR, version 3.0. In what follows, we describe AD methods in the context of their use for a hydrocode. We then examine setup time, results, accuracy, and computer run times for three test problems obtained by ADIFOR. Finally, we outline our plans for future work.
This article is part of the following collection of related materials.
Office of Scientific & Technical Information Technical Reports
Reports, articles and other documents harvested from the Office of Scientific and Technical Information.
Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.
HENNINGER, R.; CARLE, A. & MAUDLIN, P.HYDROCODE SENSITIVITIES BY MEANS OF AUTOMATIC DIFFERENTIATION,
article,
January 1, 2001;
New Mexico.
(https://digital.library.unt.edu/ark:/67531/metadc723976/:
accessed March 18, 2024),
University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.