Effects of model resolution on optimal design of subsurface flow and transport problems

Mathematical modeling of water resources problems is regularly undertaken to aid the management or design of a system. These optimal design problems can require a large number of model simulations with different sets of design variables. In an effort to reduce the computational expense of such design problems, various sources of error are typically introduced into the numerical model simulations, often without explicit consideration of subsequent effects on solution quality. We investigate several sources of such errors, including model formulation, grid resolution, and solver error for a set of community test problems, which have received attention in the literature as a vehicle to evaluate and evolve optimization methods. Results show that common shortcuts used to reduce computational effort can lead to inaccurate solutions that differ quantitatively and qualitatively from optimal solutions found using highly resolved methods. In addition to highlighting what we believe is a common issue, we present improved solutions to the problems considered, identify alternative model and optimization formulations that give equivalent accuracy with reduced computational effort, and provide guidance for improving generally the reliability of optimal design solutions to water resources problems.