• Shrikrishna Dasari
• Amit Parikh

In this research, we offer a useful and accurate numerical method for studying pollutant movement in one-dimensional water channels, employing a well-known Burgers' equation as a standard. Rather than relying on existing conventional grid-based methods, this method constructs a set of meshless formulations based on the Radial Basis Functions (RBFs), focusing on the Multiquadric type, to represent spatial derivatives. The classic fourth-order Runge–Kutta method is used for the time integration. By removing these restrictions, this selection enables the use of the method in more complex or irregular domains. A convergence study and the Method of Manufactured Solutions (MMS) are performed on the outcomes to ensure their reliability. Grid refinement is utilized to show rapid error reduction, and there is excellent correspondence of the method with the manufactured solution, indicating a high order of accuracy. In addition, it significantly exhibits the capability in dealing with the nonlinear advection-diffusion characteristic of pollutant dynamics. The proposed RBF methodology is precise, adaptable, and efficient, thus, it has a lot of potential for wide use in environmental flow simulation and actual water quality modeling.

Meshless RBF, Burgers’ Equation, Pollutant Transport, MMS, Convergence Analysis

"Numerical Simulation of Pollutant Transport in Water Channels Using Meshless Radial Basis Functions and Burgers’ Equation", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 12, page no.224-231, December-2025, Available :http://www.jetir.org/papers/JETIRHE06028.pdf

"Numerical Simulation of Pollutant Transport in Water Channels Using Meshless Radial Basis Functions and Burgers’ Equation", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 12, page no. pp224-231, December-2025, Available at : http://www.jetir.org/papers/JETIRHE06028.pdf