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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| Format: | Article |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/1/93 |
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| author | Geovanny Gordillo Mario Morales-Hernández Pilar García-Navarro |
| author_facet | Geovanny Gordillo Mario Morales-Hernández Pilar García-Navarro |
| author_sort | Geovanny Gordillo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:31:59Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:31:59Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-8da08faaed584eab8aef1ac130ec69472023-11-23T11:54:00ZengMDPI AGMathematics2227-73902021-12-011019310.3390/math10010093Solute Transport Control at Channel Junctions Using Adjoint SensitivityGeovanny Gordillo0Mario Morales-Hernández1Pilar García-Navarro2Fluid Mechanics, EINA-I3A, Universidad de Zaragoza, C/María de Luna 3, 50018 Zaragoza, SpainFluid Mechanics, EINA-I3A, Universidad de Zaragoza, C/María de Luna 3, 50018 Zaragoza, SpainFluid Mechanics, EINA-I3A, Universidad de Zaragoza, C/María de Luna 3, 50018 Zaragoza, SpainWater 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.https://www.mdpi.com/2227-7390/10/1/93adjointgradient-descentjunctionstransport equation |
| spellingShingle | Geovanny Gordillo Mario Morales-Hernández Pilar García-Navarro Solute Transport Control at Channel Junctions Using Adjoint Sensitivity Mathematics adjoint gradient-descent junctions transport equation |
| title | Solute Transport Control at Channel Junctions Using Adjoint Sensitivity |
| title_full | Solute Transport Control at Channel Junctions Using Adjoint Sensitivity |
| title_fullStr | Solute Transport Control at Channel Junctions Using Adjoint Sensitivity |
| title_full_unstemmed | Solute Transport Control at Channel Junctions Using Adjoint Sensitivity |
| title_short | Solute Transport Control at Channel Junctions Using Adjoint Sensitivity |
| title_sort | solute transport control at channel junctions using adjoint sensitivity |
| topic | adjoint gradient-descent junctions transport equation |
| url | https://www.mdpi.com/2227-7390/10/1/93 |
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