Open Boundary Control Problem for Navier-Stokes Equations Including a Free Surface: Adjoint Sensitivity Analysis

Authors:
I. Yu. Gejadze;G. J. M. Copeland
Affiliations:
Department of Civil Engineering, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow, G4 0NG, U.K.;Department of Civil Engineering, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow, G4 0NG, U.K.
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 3
Cited 3

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Original article: Estimation of spatially varying open boundary conditions for a numerical internal tidal model with adjoint method

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Abstract

This paper develops the adjoint sensitivities to the free-surface barotropic Navier- Stokes equations in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution by open-boundary control. To calculate a variation in a surface variable, a mapping is used in the vertical to shift the problem into a fixed domain. A variation is evaluated in the transformed space from the Jacobian matrix of the mapping. This variation is then mapped back into the original space where it completes a tangent linear model. The adjoint equations are derived using the scalar product formulas redefined for a domain with variable bounds. The method is demonstrated by application to an unsteady fluid flow in a one-dimensional open channel in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface (a 2D vertical section model). This requires the proper treatment of open boundaries in both the forward and adjoint models. A particular application is to the construction of a fully three-dimensional coastal ocean model that allows assimilation of tidal elevation and current data. However, the results are general and can be applied in a wider context.