<![CDATA[Pollutant transport in water is a global issue commonly modeled using advection-diffusion equations that describe transport driven by concentration gradients and flow velocity. Because analytical solutions are limited to simple cases, numerical methods are essential for simulating pollutant transport. However, many existing numerical models require complex formulations to achieve accurate, stable solutions. This study proposes a one-dimensional numerical model based on a modified Lax scheme combined with the Hansen filter, providing stable, accurate solutions with a simpler formulation. The proposed model is evaluated using three test cases: pure advection, advection-diffusion, and a Gaussian pulse. The performance of the proposed numerical model is compared with the exact solution using L2, L?, and absolute error analysis. For the pure advection case, the proposed model achieves L2=0.048 and L?=0.011, which are lower than those reported by some previous numerical models. In the advection-diffusion case, the model also has better accuracy than some previous numerical models with L2=0.0948 and L?=0.0422. For the Gaussian pulse case, the absolute error remains very small at 8.76 × 10-5 at the concentration peak. show that the proposed model can suppress numerical oscillations while maintaining high accuracy and efficiency, making it effective for one-dimensional simulations of pollutant transport.]]>
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