WATER RESOURCES RESEARCH GRANT PROPOSAL

**Project ID:** 2004AZ68G

**Title:** Forward
and Inverse Transient Analytic Element Models of Groundwater Flow

**Project Type:** Research

**Focus Categories: **Groundwater,
Hydrology, Models

**Keywords:** Groundwater,
Flow, Transient, Heterogeneity, Three-dimensional, Forward Modeling, Inverse
Modeling, Analytic Element, Laplace Transform, Parallel Computation, Visualization

**Start Date: **09/01/2004

**End Date: **08/31/2007

**Federal Funds:**
$131,976

**Non-Federal Matching Funds: **$134,003

**Congressional District: **7th

**Principal Investigator: **

Shlomo P. Neuman

**Abstract**

The Problem: To understand and quantify the groundwater component of the hydrologic cycle and to manage groundwater resources in an optimal and sustainable manner, it is necessary to model transient groundwater flow in three spatial dimensions. Traditional finite difference and finite element models require a fine computational grid to accurately represent subsurface heterogeneity and complex flow fields, rendering them computationally demanding. Practical applications of groundwater models require the ability of the analyst to readily modify the model setup for evaluating different scenarios, to complete the numerical calculations in a short amount of time, and to visualize the model results. Development of an efficient and accurate computational algorithm and graphical visualization software will greatly enhance the effective use of groundwater models.

A Promising Solution: The analytic element method (AEM) is a mesh-free, highly accurate and computationally efficient mathematical modeling technique. It makes use of analytical solutions corresponding to discontinuities, inhomogeneities and sources associated with linear (or linearized) groundwater flow equations. Its major drawback has been inability to deal effectively with transient flow. Attempts to develop transient versions of the AEM have required sacrificing some of its most attractive features. Recently Furman and Neuman (2003, 2004) proposed a new Laplace transform analytic element method (LT-AEM) for the solution of transient groundwater flow problems. In LT-AEM, AEM is applied in Laplace space and the results transformed numerically back into the time domain. LT-AEM preserves all advantages of the AEM in Laplace space, most importantly its mathematical elegance, accuracy and mesh-free nature. Solution in Laplace space and numerical back transformation into the time domain are done independently for any given discrete value of the Laplace transform parameter and for any given time, rendering LT-AEM amenable to highly efficient parallel computation on multiple processors. The method is particularly well suited for cases where a high-accuracy solution is required at a relatively small number of discrete space-time locations.

Goal and Objectives: Our goal is to build on the ideas of Furman and Neuman (2003, 2004) by developing novel forward and inverse analytic element modeling concepts and tools for transient two- and three-dimensional groundwater flow in complex and heterogeneous hydrogeologic environments. To achieve it, we propose to purse the following specific objectives: 1) Develop mathematical expressions for transient two- and three-dimensional, spherical and elliptical elements suitable for incorporation into LT-AEM; 2) develop mathematical expressions for transient two- and three-dimensional line, area and volume source and dipole elements suitable for incorporation into LT-AEM; 3) develop a capability of handling nonzero initial conditions by adding a solution of a corresponding Poisson equation, and solving the latter via the AEM, as proposed by Furman and Neuman (2003, 2004); 4) develop sequential and parallel computational LT-AEM algorithms, user-friendly software, and easy-to-use visualization tools for the forward prediction of transient two- and three-dimensional groundwater flow incorporating the elements and capabilities developed under Objectives 1 – 3; 5) implement the software on a number of realistic case examples and explore its flexibility, accuracy and computational efficiency; 6) develop a statistically-based inverse algorithm to estimate parameters entering into our LT-AEM software.

Results and Benefits: A highly accurate and conceptually simple mesh-free alternative to forward and inverse modeling of transient groundwater flow in realistically heterogeneous and complex hydrogeologic environments in two and three dimensions. User-friendly software and visualization tools suitable for personal computers as well as parallel machines.

URL: http://water.usgs.gov/wrri/04grants/national/2004AZ68G.html

Last Updated: Wednesday July 13, 2005 6:29 PM

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