Upscaling and Inverse Modeling of Groundwater Flow and Mass ...

xxiv LIST OF FIGURES
2.7 Flow comparison at the fine and coarse scales using simple averaging
upscaling approaches. All circles within the dashed lines
correspond to coarse scale values that deviate less than 10%
from the reference ones; similarly, all circles within the outer
solid lines correspond to coarse scale values that deviate less
than 40%. The average relative bias, as defined in Equation
2.10, is reported in the lower right corner of each box. . . . . . 25
2.8 Longitudinal mass distribution profiles of the tritium plume
from the fine scale reference realization, and predictions by some
simple averaging upscaling approaches at the coarse scale for
t = 328 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.9 Flow comparison at the fine and coarse scales using Laplacianbased
upscaling approaches. All circles within the dashed lines
correspond to coarse scale values that deviate less than 10%
from the reference ones; similarly, all circles within the outer
solid lines correspond to coarse scale values that deviate less
than 40%. The average relative bias, as defined in Equation
2.10, is reported in the lower right corner of each box. . . . . . 27
2.10 Longitudinal mass distribution profiles of the tritium plume
from the fine scale reference realization, and predictions on uniform
and non-uniform coarse scale grids, for t = 328 days. . . 28
2.11 Longitudinal mass distribution profiles of the tritium plume
from the fine scale reference realization, and predictions by some
Laplacian-based upscaling approaches at the coarse scale, for
t = 328 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.12 Transport in the fine scale reference realization for t = 328
days. (A) Depth-integrated normalized concentration distribution.
(B) Laterally-integrated normalized concentration distribution.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.13 Transport at the coarse scale after upscaling the reference realization
on a uniform grid using a block-centered simple-Laplacian
approach for t = 328 days. (A) Depth-integrated normalized
concentration distribution. (B) Laterally-integrated normalized
concentration distribution. . . . . . . . . . . . . . . . . . . . . . 30
2.14 Transport at the coarse scale after upscaling the reference realization
on a uniform grid using an interblock-centered simple-
Laplacian approach for t = 328 days. (A) Depth-integrated
normalized concentration distribution. (B) Laterally-integrated
normalized concentration distribution. . . . . . . . . . . . . . . 31