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

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.