Department of Mechanical and Aerospace Engineering

Daniel Tartakovsky › Publications › lu-2000-direct

Z. M. Lu, S. P. Neuman, A. Guadagnini and D. M. Tartakovsky, "Direct solution of unsaturated flow in randomly
heterogeneous soils", in *Computational Methods in Water Resources,
Vols. 1 and 2:
Computational Methods for Subsurface Flow
and Transport - Computational Methods,
Surface Water Systems and Hydrology,
Eds. L.R. Bentley,
J.F. Sykes, C.A. Brebbia,
W.G. Gray, G.F. Pinder
(Proceedings of the XIII
International Conference
"Computational Methods
in Water Resources")*, (Calgary, Canada, June 25-29), pp. 785-792, Jun 2000

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We consider steady state unsaturated flow in bounded
randomly heterogeneous soils under the influence of random
forcing terms. Our aim is to predict pressure heads and fluxes
without resorting to Monte Carlo simulation, upscaling or
linearization of the constitutive relationship between
unsaturated hydraulic conductivity and pressure head. We
represent this relationship through Gardner's exponential model,
treating its exponent alpha as a random constant and saturated
hydraulic conductivity, *K _{s}*,
as a spatially correlated random field. This allows us to
linearize the steady state unsaturated flow equations by means
of the Kirchhoff transformation, integrate them in probability
space, and obtain exact integro-differential equations for the
conditional mean and variance-covariance of transformed pressure
head and flux. We solve the latter for flow in the vertical
plane, with a point source, by finite elements to second-order
of approximation. Our solution compares favorably with
conditional Monte Carlo simulations, even for soils that are
strongly heterogeneous.

@inproceedings{lu-2000-direct,

author = {Z. M. Lu and S. P. Neuman and A. Guadagnini and D. M. Tartakovsky},

title = {Direct solution of unsaturated flow in randomly
heterogeneous soils},

year = {2000},

month = Jun,

booktitle = {Computational Methods in Water Resources,
{V}ols. 1 and 2:
{C}omputational Methods for Subsurface Flow
and Transport - {C}omputational Methods,
Surface Water Systems and Hydrology,
{E}ds. {L.R. B}entley,
{J.F. S}ykes, {C.A. B}rebbia,
{W.G. G}ray, {G.F. P}inder
({P}roceedings of the XIII
{I}nternational {C}onference
"{C}omputational {M}ethods
in {W}ater {R}esources")},

address = {Calgary, Canada, June 25-29},

pages = {785-792}

}