Abstract
Hydraulic phenomena in open-channel flows are usually described by means of the shallow water equations. This hyperbolic non-linear system can be used for predictive purposes provided that initial and boundary conditions are supplied and the roughness coefficient is calibrated. When calibration is required to fully pose the problem, several strategies can be adopted. In the present work, an inverse technique, useful for any of such purposes, based on the adjoint system and gradient descent is presented. It is used to find the optimal time evolution of the inlet boundary condition required to meet the 20 measured water depth data in an experimental test case of unsteady flow on a beach. The partial differential systems are solved using an upwind finite volume scheme. Several subsets of probes were selected and the quality of the reconstructed boundary tested against the experimental results. The results show that the adjoint technique is useful and robust for these problems, and exhibits some sensitivity to the choice of probes, which can be used to properly select probes in real applications.
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Acknowledgements
Authors would like to thank Dr. Alessandra Saponieri for the access to the experimental background and data used in this work. This worked has been partially funded by the Spanish Ministry of Innovation and Science trough research project BIA2011-30192-C02-01.
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Lacasta, A., Caviedes-Voullieme, D., García-Navarro, P. (2019). Application of the Adjoint Method for the Reconstruction of the Boundary Condition in Unsteady Shallow Water Flow Simulation. In: Minisci, E., Vasile, M., Periaux, J., Gauger, N., Giannakoglou, K., Quagliarella, D. (eds) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-89988-6_10
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DOI: https://doi.org/10.1007/978-3-319-89988-6_10
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