Two-Dimensional Modeling of Fractional Advection-Dispersion Equation using Meshfree Local Petrov-Galerkin Numerical Method (Case Study: Athabasca River)

The study of surface water quality has special importance. Unfortunately, sometimes sewage and industrial effluents are discharged into the river. If the mechanism of transport and diffiusion of pollution in rivers with different geometry is known, it can be planned to reduce the effects of pollution on the general health of human society by raising the issue of water mixing and strengthening the self-purification of rivers. The governing equation over the pollution transport phenomenon in rivers is advection-dispersion equation. This equation is classic and does not have the necessary accuracy in predicting the amount of pollutant concentration in the river; Therefore, this equation must be changed in such a way to have the least error in the simulation. The fractional calculus method is used to accurately investigate the transport of pollutants in the stream. To model the pollutant transport in the river, differential equation must be solved. Meshless method is one of the newest numerical methods in recent years that was able to correct some of the disadvantages of mesh-based methods. Studies show that the most studies have focused on solute transport in steady-state flow regimes and regular cross-sections. This study seeks to provide a comprehensive model for simulating the phenomenon of pollutant transport in rivers with steady and non-uniform flow to eliminate the shortcomings of common models. In this study, the parameters of dispersion coefficients, fractional order derivatives and skewness coefficients were optimized in the longitudinal and transverse directions. The values of dispersion coefficient in the longitudinal and transverse directions were 68 and 2.5 m2/s, respectively. The output of the proposed model was compared with the observational data of the Athabasca River and the Mike21 model for three cross sections. The results showed that the amount of R2 in the Meshless Local Petrovo-Galerkin method increased by an average of 11% compared to the Mike model.