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

Shallow water equations and its Adjoint
Adjoint
∂η
∂t + Ū ∂η
∂x + ¯V ∂η
∂y + H ∂u′
∂x + H ∂v ′
∂y
∂u ′
∂t + Ū ∂u′
∂x + ¯V ∂u′
∂y + g ∂η
∂x
∂v ′
∂t + Ū ∂v ′
∂x + ¯V ∂v ′
∂y + g ∂η
∂y
= 0
= 0
= 0
∂φ
∂τ − Ū ∂φ
∂x − ¯V ∂φ
∂y − g ∂ψ 1
∂x − g ∂ψ 2
∂y + ∂r
∂η
= 0
∂ψ 1
∂τ − Ū ∂ψ 1
∂x − ¯V ∂ψ 1
∂y − H ∂φ
∂x + ∂r
∂u ′ = 0
∂ψ 2
∂τ − Ū ∂ψ 2
∂x − ¯V ∂ψ 2
∂y − H ∂φ
∂y + ∂r
∂v ′ = 0
Vani Cheruvu (ASP Research Review) Adjoint Sensitivity Analysis 06/14/2007 14 / 30