Optimization-based simulation and design of tile drainage systems

Optimization-based models for simulation of the drainage systems are formulated and solved with a finite-difference approximated Richard's equation as an embedded constraint. The solution methodology minimizes the sum of absolute violations off the discretized variably saturated porous media flow equations. The optimal design minimizes the sum of the pressure heads to obtain optimal drain locations and discharges for a given lateral spacing. The projected augmented Lagrangian method of nonlinear programming is used to solve the optimization models. The performance of the simulation is verified using the steady-state square embankment drainage problem. Thereafter, the simulation and design models are solved for a hypothetical tile drainage system. The results demonstrate the capability of the models.