Solute Transport Control at Channel Junctions Using Adjoint Sensitivity

Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking into account that mo...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-01, Vol.10 (1), p.93
Main Authors: Gordillo, Geovanny, Morales-Hernández, Mario, García-Navarro, Pilar
Format: Article
Language:English
Subjects:
adjoint
Boundary conditions
Channel flow
Contaminants
Eigenvalues
Finite volume method
gradient-descent
Iterative methods
junctions
Mathematical analysis
Quality control
Rivers
Sensitivity
Shallow water equations
Simulation
transport equation
Transport equations
Water quality
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Summary:Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking into account that most channels and rivers include junctions with other branches, the objective of this study is to explore the adjoint technique on a channel network to reconstruct the upstream boundary condition of the convection-reaction equation. For this purpose, the one-dimensional shallow water equations and the transport equation for a reactive solute are considered. The control is formulated through the gradient-descent technique supplied with a first-order iterative process. Both the physical and the adjoint equations are supplied with suitable internal boundary conditions at the junction and are numerically solved using a finite volume upwind scheme. The results reveal that the adjoint technique is capable of reconstructing the inlet solute concentration boundary condition in an acceptable number of iterations for both steady state and transient configurations using a downstream measurement location. It was also observed that the reconstruction of the boundary condition tends to be less effective the further away the measurement station is from the target.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10010093