Abstract
This work presents an approach to solve inverse problems in the application of water quality management in reservoir systems. One such application is contaminant cleanup, which is challenging because tasks such as inferring the contaminant location and its distribution require large computational efforts and data storage requirements. In addition, real systems contain uncertain parameters such as wind velocity; these uncertainties must be accounted for in the inference problem. The approach developed here uses the combination of a reduced-order model and a Bayesian inference formulation to rapidly determine contaminant locations given sparse measurements of contaminant concentration. The system is modelled by the coupled Navier-Stokes equations and convection-diffusion transport equations. The Galerkin finite element method provides an approximate numerical solution-the ’full model’, which cannot be solved in real-time. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reduced-order model that approximates the full model. The Bayesian formulation of the inverse problem is solved using a Markov chain Monte Carlo method for a variety of source locations in the domain. Numerical results show that applying the reduced-order model to the source inversion problem yields a speed-up in computational time by a factor of approximately 32 with acceptable accuracy in comparison with the full model. Application of the inference strategy shows the potential effectiveness of this computational modeling approach for managing water quality.
Highlights
Hydrodynamic processes such as contaminant transport in lakes and reservoirs have a direct impact on water quality
We assume that the contaminant is present within the main reservoir section and that the contaminant transport processes are mainly affected by the inflow and wind velocity
This study has applied successfully the combination of a model order reduction technique based on the Proper orthogonal decomposition (POD) and a Bayesian inference approach to solve an inverse problem that seeks to identify an uncertain contaminant location
Summary
Hydrodynamic processes such as contaminant transport in lakes and reservoirs have a direct impact on water quality. Because of some processes such as convection, diffusion, time rate release of contaminants, and distance of travel. To simulate such processes, a coupled system of partial differential equations (PDEs) including the Navier-Stokes equations (NSEs) and contaminant transport equations needs to be solved. The direct or forward problems compute the distribution of contaminant directly from given input information such as contaminant location, contaminant properties, fluid flow properties, boundary conditions, initial conditions, etc. The inverse problems infer the unknown physical parameters, boundary conditions, initial conditions, or geometry given a set of measured data. These known data can be obtained experimental or computational.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
