Sensitivity Analysis for Shallow Water Equations - Advanced Study ...

Shallow Water Equations
Objective Function
∂η
∂t + ∂(Hu′ + Ūη)
∂x
∂u ′
∂t + ∂(Ūu′ + gη)
∂x
= 0
= 0
J =
∫ T ∫ L
0
0
r(η, u ′ ; x, t)dxdt
t= time; x = distance along the channel; η = depth of flow;
u ′ = discharge per unit width; r = user-defined measuring function
r = 1 2 [η(x 0, t) − ¯η(x 0 )] 2 δ(x − x 0 )
Vani Cheruvu (ASP Research Review) Adjoint Sensitivity Analysis 06/14/2007 11 / 30