Gugat M (2007)
Publication Language: English
Publication Type: Book chapter / Article in edited volumes
Publication year: 2007
Publisher: Birkhäuser
Edited Volumes: International Series of Numerical Mathematics
Series: Control of Coupled Partial Differential Equations
City/Town: Basel
Book Volume: 155
Pages Range: 69-94
ISBN: 978-3-7643-7721-2
URI: http://link.springer.com/chapter/10.1007/978-3-7643-7721-2_4
DOI: 10.1007/978-3-7643-7721-2_4
In active flood hazard mitigation, lateral flow withdrawal is used to reduce the impact of flood waves in rivers. Through emergency side channels, lateral outflow is generated. The optimal outflow controls the flood in such a way that the cost of the created damage is minimized. The flow is governed by a networked system of nonlinear hyperbolic partial differential equations, coupled by algebraic node conditions. Two types of integrals appear in the objective function of the corresponding optimization problem: Boundary integrals (for example, to measure the amount of water that flows out of the system into the floodplain) and distributed integrals.
For the evaluation of the derivative of the objective function, we introduce an adjoint backwards system. For the numerical solution we consider a discretized system with a consistent discretization of the continuous adjoint system, in the sense that the discrete adjoint system yields the derivatives of the discretized objective function. Numerical examples are included.
APA:
Gugat, M. (2007). Optimal Boundary Control in Flood Management. In Karl-Heinz Hoffmann, Günter Leugering, Michael Hintermüller (Eds.), International Series of Numerical Mathematics. (pp. 69-94). Basel: Birkhäuser.
MLA:
Gugat, Martin. "Optimal Boundary Control in Flood Management." International Series of Numerical Mathematics. Ed. Karl-Heinz Hoffmann, Günter Leugering, Michael Hintermüller, Basel: Birkhäuser, 2007. 69-94.
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