Multiscale optimal control of in Situ bioremediation

Multiscale methods have been demonstrated to be highly efficient techniques for solving partial differential equations. In this paper, the idea of applying multiscale computation to an optimal control model of groundwater in situ bioremediation is investigated. The optimal control model, which was developed in previous work, uses an optimal control method called successive approximation linear quadratic regulator to identify optimal well locations and pumping rates to minimize pumping costs. The model can be used as an aid in designing more cost-effective aerobic in situ bioremediation, where injection wells are used to supply oxygen and extraction wells are used to contain the contaminant plume. The goal of this research is to improve the computational efficiency of the model so that complex field sites can be addressed. A spatial multiscale approach is presented in this paper. The spatial multiscale concept comes from discretization of the model domain with different mesh sizes. By solving the optimization on different numerical meshes and using bilinear interpolation operator to switch from the coarser mesh to finest mesh, significant computational savings can be gained. Both the convergence behavior and CPU time are presented for a case study under homogeneous conditions. The impact and choice of penalty weight when applying the multiscale approach are also discussed.