A model predictive control (MPC)-integrated multiphase immersed boundary (IB) framework for simulating wave energy converters (WECs)

In this work, we present a novel MPC-integrated multiphase IB framework that can compute the optimal energy-maximizing control force on-the-fly by dynamically interacting with a high-fidelity numerical wave tank (NWT). Due to the requirement of solving a constrained optimization problem at each time step of the IB simulation, the MPC algorithm utilizes a low-dimensional dynamical model of the device that is based on the linear potential theory (LPT). The multiphase IB solver, on the other hand, is based on the high-dimensional fictitious domain Brinkman penalization (FD/BP) method, which fully-resolves the hydrodynamic nonlinearities associated with the wave-structure interaction (WSI). A time-series forecasting auto-regressive model is implemented that predicts wave heights to estimate the future wave excitation/Froude- Krylov forces for the MPC algorithm. Moreover, we also experiment with non-linear Froude-Krylov (NLFK) forces for the first time in an MPC formulation. Under varying sea conditions, the predictions of the MPC-integrated multiphase IB solver are compared to the widely popular LPT-based solvers. Overall, six WSI/MPC solver combinations are compared for a heaving vertical cylinder. We also determine the pathway of energy transfer from the waves to the power take-off (PTO) system and verify the relationships using IB simulations. Additionally, three different sea states are simulated within the IB simulation to test the adaptive capability of MPC for WECs. MPC is demonstrated to adapt to changing sea conditions and find the optimal solution for each sea state.