10.4122/1.1000000723
Fowler, Kathleen
Kathleen
Fowler
kfowler@clarkson.edu
Gray, Genetha
Genetha
Gray
gagray@sandia.gov
Gray, Genetha
Genetha
Gray
gagray@sandia.gov
Approaching the Groundwater Remediation Problem Using Multifidelity Optmization
XVI International Conference on Computational Methods in Water Resources
2006
2006
The objective of the hydraulic capture method for optimal groundwater remediation
design is containment of a contaminant plume using barrier wells to reverse the
direction of groundwater flow. Finding a solution involves applying optimization
algorithms in conjunction with simulators for groundwater flow and possibly for
contaminant transport. The formulation of the objective function and its
corresponding constraints dictates which optimization algorithms are appropriate and
usually eliminates gradient based approaches from consideration. In addition,
objective functions and constraints can be nonlinear, non-convex, non-
differentiable, or even discontinuous, and the simulations involved can be
computationally expensive.
Both computational efficiency and accuracy are important, and this further
influences the choice of solution method. With the advent and increasing
availability of massively parallel computers, computational speed has increased
tremendously. Unfortunately, the numerical and model complexities of problems like
groundwater remediation still demand significant computational resources. Moreover,
these expenses can be a limiting factor of optimization since obtaining solutions
often requires the completion of numerous computationally intensive jobs.
Therefore, we propose an algorithm designed to improve the computational efficiency
of an optimization method for a wide range of applications and apply it to
groundwater remediation.
Our approach takes advantage of the interactions between multifidelity models and is
applicable to problems for which models of varying fidelity are available. The
method can be described as follows: First, a direct search method is applied to the
high fidelity model over a reduced design space. In conjunction with this search, a
specialized oracle is employed to map the design space of this high fidelity model
to that of a computationally cheaper low fidelity model using space mapping
techniques. Then, in the low fidelity space, an optimum is obtained using gradient
based optimization, and it is mapped back to the high fidelity space.
To motivate this work, we consider a hydraulic capture problem proposed in the
literature for benchmarking purposes. The problem is to minimize the cost to install
and operate a set of wells subject to constraints on the concentration of a
contaminant at specified locations in the physical domain. We solve the problem by
applying the multifidelity approach described above using only flow information for
the low fidelity model and using concentration based constraints for the high
fidelity model. We present some promising results for this preliminary problem, and
explain how we plan to extend our study by considering more representative physical
models, simulators, objective function formulations, and by incorporating real-site
data.