On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Line search algorithms with guaranteed sufficient decrease
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Computers & Mathematics with Applications
Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems
Mathematical and Computer Modelling: An International Journal
Adjoint-based optimization of PDEs in moving domains
Journal of Computational Physics
Mathematics and Computers in Simulation
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This paper develops the data-assimilation procedure in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution governed by the free-surface barotropic Navier-Stokes equations. The flow is considered in a 2D vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface. Since a possible application is to the construction of a coastal (limited area) circulation model, the open boundary control problem is the main scope of the paper. The assimilation algorithm is built on the limited memory quasi-Newton LBFGS method guided by the adjoint sensitivities. The analytical step search, which is based on the solution of the tangent linear model, is used. We process the gradients to regularize the solution. In numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements, which could be sufficient for boundary-control identification. As a result of these experiments we formulate some important practical conclusions.