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Reduced Order Methods for Environmental Marine Problems by Optimal Flow Control M. Strazzullo, F. Ballarin, R. Mosetti and G. Rozza MathLab, Mathematics Area, SISSA International School for Advanced Studies, Trieste, Italy OGS, National

  1. Reduced Order Methods for Environmental Marine Problems by Optimal Flow Control M. Strazzullo, F. Ballarin, R. Mosetti and G. Rozza MathLab, Mathematics Area, SISSA International School for Advanced Studies, Trieste, Italy OGS, National Institute of Oceanography and Experimental Geophysics, Trieste, Italy QUIET 2017, Trieste, July 19, 2017

  2. ROMs and OFCP( µ µ )s for Environmental Sciences µ Motivations • OFCP( µ µ ) are a useful mathematical model since they are suited for µ data assimilation , inverse problems , as well as uncertainty quantification and parameter estimation problems. They have a drawback: they are very demanding . • Reduced Order Methods ( ROMs ) are fast and reliable tools in order to solve those problems in a low-dimentional framework. Methodology In order to manage the OFCP( µ µ ): µ • we cast it into a saddle-point structure , • solved by a Partitioned POD-Galerkin approach, • with aggregated space and relying on affinity assumption . M. Strazzullo, F. Ballarin, R. Mosetti and G. Rozza ROMs for Environmental Marine Problems by OFCP 1/ 4

  3. ROMs applied to a Loss of Pollutant in the Gulf of Trieste Results of the simulated loss of pollutant in the Gulf of Trieste . Data : collected in loco. (a) Satellite image: Gulf (b) Convergence error: FE of Trieste. vs ROMs. (c) Uncontrolled concentration. (d) Controlled concentration (ROMs). M. Strazzullo, F. Ballarin, R. Mosetti and G. Rozza ROMs for Environmental Marine Problems by OFCP 2/ 4

  4. ROMs applied to a Solution Tracking on the North Atlantic Ocean Results of the solution tracking of North Atlantic Ocean current. Data : collected in loco and from simulation. (e) Satellite image and (f) Convergence error: FE mesh: Florida peninsula. vs ROMs. (g) FE Stream-function. (h) RB Stream-function. M. Strazzullo, F. Ballarin, R. Mosetti and G. Rozza ROMs for Environmental Marine Problems by OFCP 3/ 4

  5. References F. Ballarin, A. Manzoni, A. Quarteroni, and G. Rozza. Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations. International Journal for Numerical Methods in Engineering , 102(5):1136–1161, 2015. J. S. Hesthaven, G. Rozza, and B. Stamm. Certified reduced basis methods for parametrized partial differential equations. SpringerBriefs in Mathematics , 2015, Springer, Milano. F. Negri, A. Manzoni, and G. Rozza. Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations. Computers & Mathematics with Applications , 69(4):319–336, 2015. Acknowledgements We acknowledge the support by European Union Funding for Research and Innovation – Horizon 2020 Program – in the framework of European Research Council Executive Agency: H2020 ERC CoG 2015 AROMA-CFD project 681447 “Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics” (PI G. Rozza). We also acknowledge the INDAM-GNCS project “Metodi numerici avanzati combinati con tecniche di riduzione computazionale per PDEs parametrizzate e applicazioni”. M. Strazzullo, F. Ballarin, R. Mosetti and G. Rozza ROMs for Environmental Marine Problems by OFCP 4/ 4

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