Estimation of diusion and convection coecients in an aerated hydraulic jump
نویسندگان
چکیده
Diusion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection diusion partial dierential equation. The governing equation includes the diusion coecient and the convection coecient, which are taken as the control variables to minimize a domain observation type functional which evaluates the error between observed speci®c gravity and the solution to the governing equation. The minimum principle is deduced to characterize the optimal control variables using the adjoint partial dierential equation. Solvability of the partial dierential equations is discussed in terms of variational problems. An iterative numerical procedure including a ®nite element scheme to solve the partial dierential equations is developed and demonstrated by using the observed data. Ó 2000 Elsevier Science Ltd. All rights reserved.
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