TY - JOUR
T1 - Laplace-Transform Finite Element Solution of Nonlocal and Localized Stochastic Moment Equations of Transport
AU - Eric Morales-Casique & Shlomo P. Neuman
JO - Communications in Computational Physics
VL - 1
SP - 131
EP - 161
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7675.html
KW - 
AB - <p style="text-align: justify;">Morales-Casique et al. (Adv. Water Res., 29 (2006), pp. 1238-1255) developed
exact first and second nonlocal moment equations for advective-dispersive transport
in finite, randomly heterogeneous geologic media. The velocity and concentration
in these equations are generally nonstationary due to trends in heterogeneity, conditioning
on site data and the influence of forcing terms. Morales-Casique et al. (Adv.
Water Res., 29 (2006), pp. 1399-1418) solved the Laplace transformed versions of these
equations recursively to second order in the standard deviation σY of (natural) log hydraulic
conductivity, and iteratively to higher-order, by finite elements followed by
numerical inversion of the Laplace transform. They did the same for a space-localized
version of the mean transport equation. Here we recount briefly their theory and algorithms;
compare the numerical performance of the Laplace-transform finite element
scheme with that of a high-accuracy ULTIMATE-QUICKEST algorithm coupled with
an alternating split operator approach; and review some computational results due to
Morales-Casique et al. (Adv. Water Res., 29 (2006), pp. 1399-1418) to shed light on
the accuracy and computational efficiency of their recursive and iterative solutions in
comparison to conditional Monte Carlo simulations in two spatial dimensions.</p>