A Time Adaptive Grid on the QUAL2E Water Quality Model.
Water quality models are used extensively for maintaining and monitoring the waste assimilative capacity of water bodies when these bodies are exposed to contaminant inputs. Because of the sensitivity of DO concentrations over temporal and spatial steps, an accurate time dependent solution is required from the finite-difference model. To maintain numerical accuracy and efficiency, it is well known that the smaller the grid size, the more accurate the solution will be because of the decrease in the local truncation error. But this will lead to an excessive number of grid points requiring an increase in computational time. The opposite practice would be to decrease the computational time by decreasing the number of grid points. Of course, this will decrease the accuracy of the solution. Local grid clustering about areas of large physical gradients can help to solve this dilemma.
The first step in utilizing an adaptive grid in conjunction with a water quality model is to incorporate a grid generation technique that will adequately discretize the physical domain. However, this is often difficult to do since the initial physics of the solution are unknown and the initial grid may be unsuitable for the solution needed. An adaptive grid generator can concentrate the grid lines in areas where physical gradients are large, and disperse lines where the gradients are smooth. Since the accuracy of the finite-difference solution is dependent upon the suitability of the grid used to compute the solution, the adaptive grid can help to increase the accuracy of the solution. Using an elliptic grid generator based upon the Poisson equations, control functions can be fashioned to control the spacing and orientation of the coordinate grid lines, thus achieving the adaptive grid. A time dependent solution is often used in water quality modelling. However, the solution over the domain will change as time marches forward. Therefore, a dynamically adaptive grid generator is incorporated to follow the large physical gradients in time. A dynamically adaptive grid generator is a very powerful tool for time dependent solutions.
The purpose of this research is to modify an existing water quality model to perform more accurate, more representative calculations in tracking gradients in water quality variables. The model utilized in the research is The Enhanced Stream Water Quality Model QUAL2E distributed by the USEPA (Brown and Bamwell, 1987). In this model's original form, the grid lengths are set initially by the user to a uniform spacing across a stream reach, thus introducing the possibility of errors and inaccuracies in computation in areas of large physical water quality gradients. This model will be modified to have the initial grid generated automatically with a Poisson type elliptic grid generator with user specified packing capabilities. For this study, the flow rate of the point source remains constant throughout the simulation. Unsteady water quality simulations will have the dynamically adaptive grid generation technique incorporated to accurately track all pertinent physical gradients, and the model will be converted to a multi-block computational environment with accurate time-differencing across block boundaries. These modifications will enable the QUAL2E model to more accurately simulate water quality variables over a variety of different physical and temporal situations.
The QUAL2E model is a basic one dimensional advection-dispersion mass transport model, numerically integrated over space and time for each physical water quality variable. For this research, no changes were made to the latter two elemental relationships of hydrogeometric and biokinetic properties. However, the mass transport relationships have to be modified to handle the general curvilinear coordinate system. All relationships of the water quality model represented by PDE’s must be converted to the general curvilinear coordinate system.
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