Uncertainty Quantification for Multiscale Simulations

[+] Author and Article Information
B. DeVolder, J. W. Grove, K. Pao, D. H. Sharp

Los Alamos National Laboratory, Los Alamos, NM 87545

J. Glimm

Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600Center for Data Intensive Computing, Brookhaven National Laboratory, Upton, NY 11973

Y. Kang, Y. Lee, K. Ye

Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600

J. Fluids Eng 124(1), 29-41 (Nov 12, 2001) (13 pages) doi:10.1115/1.1445139 History: Received August 07, 2001; Revised November 12, 2001
Copyright © 2002 by ASME
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Grahic Jump Location
Left: Fine grid and several coarse grid solutions. Here fractional oil production rate (oil cut) is plotted vs. a dimensionless time variable, the total pore volumes of fluid injected, or PVI. Right: Typical errors (lower curves) and discrepancies (upper curves) plotted vs. PVI. The two families of curves on the right are clearly separable.
Grahic Jump Location
Illustration of the window method to construct the posterior ensemble. Left: full ensemble of oil cut curves. Right: Posterior ensemble defined as those geologies whose oil cut curves agree with the solution for geology j0 within the window error, for the past times.
Grahic Jump Location
Test problem. A piston-driven shock moves to the right. The shock is incident on a contact discontinuity, where it produces a reflected and a transmitted shock. A reflecting wall is placed at the downstream end of the shock tube. All parameters of the problem are fixed (deterministic) except the shock velocity and the contact position. Each of these are allowed a uniform variation by ±10 percent about a base value.
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A space time plot of the logarithm of density for one of the step up cases, selecting the base case from the ensemble. The finest grid result (1000 cells) is displayed.
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A space time plot of the mean error in the logarithm of density, integrated over the ensemble, step up case, finest coarse grid errors
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Histograms of space-time averaged errors. Upper left: the specific internal energy error field. The boxes from left to right show regions centered about the reflected shock, deflected contact, and transmitted shock respectively. HISTOGRAMS: Upper right—reflected shock region. Lower left—contact region, Lower right—transmitted shock region. The solid and dashed curves show the kernel density estimate and the best Gaussian fit to the distributions respectively.
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Left: mean errors as a function of time for the contact location for three levels of grid refinement. Right: histogram of errors in the shock arrival time at the wall, for Δx=0.05.
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Time dependence of the localized specific internal energy error for Δx=0.05



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