Low Order Optimal Control of Reservoir

Abstract

We explore an optimal control problem for the reservoir system by using reduced-order models (ROMs) based on proper orthogonal decomposition (POD). The aim is to 'flush' the containment out of the reservoir by applying the control at outflow boundaries. The objective function is to minimize a combination of control goal and containment over a certain period of time. The system model is the coupled Navier-Stokes equations and convetion-diffusion equation. Due to high computational requirements of the coupled and non-linear system, the full KTT system which is obtained from the adjoint method is too expensive to solve. The POD-based ROMs is constructed via a combination of Galerkin projection method and POD basis that directly applied to the coupled system to yield a set of ordinary differential equations capturing the essential dynamics of the system. Numerical results show that the controlled actions using ROMs provide a faster answer than using the full model. Because of the significant savings in computational costs and storage requirements and the effectiveness of the optimal control, the POD-based ROMs is able to provide a good tool for water quality management.