Sensitivity Analysis for Shallow Water Equations - Advanced Study ...
Sensitivity Analysis for Shallow Water Equations - Advanced Study ...
Sensitivity Analysis for Shallow Water Equations - Advanced Study ...
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Adjoint <strong>Sensitivity</strong> Method<br />
Derivation of 1D Adjoint <strong>Equations</strong><br />
Adjoint variables : φ(x, t) and ψ(x, t)<br />
Multiply the continuity equation by φ(x, t) and the momentum<br />
equation by ψ(x, t)<br />
The sum of these two products is then integrated over space and time<br />
Flow control is desired, hence the variation with respect to η and u ′<br />
Variation of the objective function with respect to η and u ′<br />
Add the variations<br />
Choose initial condition <strong>for</strong> the adjoint problem<br />
Choose boundary values <strong>for</strong> the adjoint variables<br />
Vani Cheruvu (ASP Research Review) Adjoint <strong>Sensitivity</strong> <strong>Analysis</strong> 06/14/2007 13 / 30
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