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.

}, address = {Basel}, author = {Gugat, Martin}, booktitle = {International Series of Numerical Mathematics}, doi = {10.1007/978-3-7643-7721-2{\_}4}, editor = {Karl-Heinz Hoffmann, Günter Leugering, Michael Hintermüller}, faupublication = {yes}, isbn = {978-3-7643-7721-2}, keywords = {St. Venant equations; subcritical states; adjoint system; optimal boundary control; necessary optimality conditions; classical solutions}, note = {UnivIS-Import:2015-04-20:Pub.2007.nat.dma.zentr.optima}, pages = {69-94}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {Control of Coupled Partial Differential Equations}, title = {{Optimal} {Boundary} {Control} in {Flood} {Management}}, url = {http://link.springer.com/chapter/10.1007/978-3-7643-7721-2{\_}4}, volume = {155}, year = {2007} }