Using one-step group preserving schemes for contaminant transport modeling in rivers

Document Type : Research Paper

Authors

1 Department of Water Engineering and Management, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran.

2 Department of Water Engineering and Management, Faculty of Agriculture, University of Tarbiat Modares, Tehran, Iran

Abstract

The recent escalation of environmental concerns necessitates the development of computer models able to predict pollutant dispersal in natural aquatic systems, rendering them an absolute essentiality. Unlike physical models, the primacy of such computer models lies in their lower costs and facile adaptability to novel conditions. In order to resolve the pollution transport equation in rivers, both directly and inversely, the Group Preserving Scheme has been employed. As expeditious simulation of the pollutant intensity function is imperative, determining a technique to achieve this with celerity is essential. Solving the pollution transport equation in one time step utilizing GPS reduces computational duration and conserves time and resources. GPS constitutes a method for solving malignant problems. This method has been leveraged to solve the one-dimensional advection-dispersion equation with variable coefficients. This method is based on solving dynamic systems in positive and negative time intervals and deriving a general equation to solve ordinary differential equations in a one-step approach. In this study, three examples are shown to demonstrate the performance of the one-step solution of the direct and inverse Group Preserving Scheme. First, the pollutant concentration in the river was calculated using the forward solution with variable coefficients. Next, two different examples were used to simulate the pollutant intensity function at the initial time, employing the Backward Group Preserving Scheme. Afterward, the accuracy of the one-step and multi-step solutions was evaluated using statistical indicators.

Keywords

Main Subjects

Using one-step group preserving schemes for contaminant transport modeling in rivers

EXTENDED ABSTRACT

Introduction:

Recent years have witnessed growing environmental worries, rendering the creation of computer models that foresee pollutant dispersal in natural aquatic systems an absolute prerequisite. As expeditious simulation of the pollutant intensity function is of the essence, determining a technique to accomplish this with alacrity is imperative.

Material and method:

The current study implements the Group Preserving Scheme (GPS), predicated on Lie groups, to resolve the pollution transport equation in rivers, both directly and inversely. Initially, GPS is elucidated for the one-step direct solution of the pollution transport equation. Subsequently, the explication of the one-step Backward Group Preserving Scheme for the one-step inverse solution of this equation is examined. Finally, the advection-dispersion equation is resolved directly and inversely utilizing this methodology in a one-step and multi-step manner, with the accuracy of these two solutions evaluated against the exact solution. In this research, as an initial phase, the direct numerical approach is employed to solve the pollution transport equation unidimensionally. The resultant outcomes are then utilized as inputs for the second phase of computations (inverse solution of the pollution transport equation) to derive the final results (pollutant intensity function). To model the transport and release of pollutants in the river using GPS, the river is divided into n intervals.

Result and Discussion:

Three test cases have been designed to evaluate the one-step solution of the pollution transport equation directly and inversely in the temporal dimension utilizing the GPS. These three modal tests are presented in sequence to demonstrate the performance of the one-step method and its comparison to the multi-step approach. Since the pollution transport equation is solved with variable coefficients herein, the flow parameters must be computed first, obtained by solving the flow equations and employing extant models. The river characteristics have been considered per the actual conditions test, and the flow parameters have been calculated using the Saint Venant equation. For superior evaluation of the one-step method, statistical error indices, including Correlation Coefficient (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Relative Error (MRE) have been utilized. In the first test case, where the simulation was performed directly, the one-step method encountered minor issues in simulating the concentration range, and the construction of the peak was also accompanied by an error, with the peak simulated by the one-step model created higher than the actual value. In the second test case involving reverse simulation, the one-step method performed relatively well compared to the multi-step method in reconstructing the concentration range and pollution peak, with minimal problems compared to the multi-step method, rendering this error negligible and the outcome expected given the one-step simulation. In the third test case intended for reverse simulation of the complex pattern, the one-step method performed remarkably well in reconstructing the peaks and correctly identified even the highest peak. The time delay in reaching peak concentration is evident in the one-step method compared to the multi-step method, engendering decreased accuracy of this method relative to the multi-step method in peak reconstruction. The accuracy of reconstructing the returned pattern by the inverse model versus the exact solution ranged from 86% to 99.8%, representing the maximum error of the one-step method during peak formation. The time delay in attaining peak concentration in the one-step method is more conspicuous in the mode 3 test than in the mode 2 test, with the complexity of the final condition as input to the inverse model not impervious to this time delay.

Conclusion:

The location of the peak is accurately identified by this method, and considering the time savings, the outcome of this method is acceptable. The delay in attaining peak concentration was observed in the reverse simulation, being more conspicuous in the more complex model. However, despite expedited and economical completion under certain conditions, a decrease in model accuracy can be overlooked, and numerical solutions utilized from this method as an efficacious and efficient approach delineated.

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Iranian Journal of Soil and Water Research
Volume 54, Issue 11
January 2024
Pages 1627-1646

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