A publication of the Office of Advanced Simulation & Computing, NNSA Defense Programs
NA-ASC-500-07—Issue 3
May 2007
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Large Dataset Generated for the Verification of an ASC Code
During March 2007 Marine Marcilhac, Division X-1 postdoc at Los Alamos (LANL), and François Hemez, X-1 technical staff member, completed 12,256 simulation runs with an ASC code to quantify numerical uncertainty. Part of the Code Verification project, headed at LANL by X-1’s Jerry Brock, the project’s goals are to develop methodologies for code and solution verification, assess time-to-solution, and quantify solution uncertainty in support of programmatic deliverables.
The investigated algorithm is a finite-volume Godunov solver for the compressible equations of hydrodynamics in Eulerian frame-of-reference, developed by the Crestone Code Project at LANL. Six test problems were analyzed (Noh, Sedov, Woodward-Corolla interactive waves, and three variants of the Sod shock tube). Although this demonstration is currently restricted to 1D geometry, the dataset includes smooth and shocked solutions, convergent and divergent flows, and various patterns of wave interaction. A computer experiment was designed to vary the grid refinement, Courant condition, time-step controls, and four other options of the numerical method. Depending on settings of the calculation and numerical method, running times for analysis of each test problem varied between 10 seconds and 8 hours, using four processors of the QSC platform at LANL. Generating such a large dataset was a significant effort that tested the ability of a toolbox developed to generate designs-of-computer-experiments; write, organize, and submit multiple input decks for parametric study; upload and post-process the results; perform effect screening and analysis-of-variance; and analyze the solution quality as a function of grid refinement.
The figure represents the L1 norms of the differences between exact and discrete solutions as a function of grid sizes used. The solution errors are shown for the density field of four test problems representing 11,552 runs. The figure illustrates two main findings of the study: (1) the numerical method is first-order accurate, as expected when discontinuous solutions, such as those of the four test problems shown, are computed; (2) solution accuracy is sensitive to the choice of numerical options used in the calculation. The figure also indicates that greater accuracy tends to be achieved at the cost of increased sensitivity to the method of performing the simulation.
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