Numerical exploration of pollutant transport using stochastic fractional diffusion and Karhunen-Loève expansion

Articles in Press

Document Type : Research Article

Authors

• Zahra Moniri ¹
• Afshin Babaei ¹
• Behrouz Parsa Moghaddam ²

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

² Department of Mathematics, La.C., Islamic Azad University, Lahijan, Iran.

10.22067/ijnao.2025.93661.1654

Abstract

‎This study explores a fractional time-space stochastic diffusion equation for modeling pollutant concentration‎, ‎incorporating Caputo fractional derivatives and fractional Laplacians to capture anomalous diffusion‎. ‎Stochastic noise‎, ‎modeled via Brownian motion and Brownian bridges‎, ‎is simulated using the Karhunen-Loève expansion‎. ‎The equation's formulation‎, ‎along with initial and boundary conditions‎, ‎is presented‎. ‎Analytical and numerical methods are discussed‎, ‎emphasizing a hybrid framework combining Fast Fourier Transform‎, ‎L1-algorithm‎, ‎and Karhunen-Loève expansion techniques‎. ‎Numerical examples with sinc and Gaussian initial conditions highlight the superior accuracy and efficiency of the KLE approach over traditional Euler methods‎, ‎revealing the significant influence of fractional parameters on pollutant dispersion dynamics and their potential for environmental modeling applications‎.

Keywords

• Non-integer order probabilistic transport equation
• Memory-dependent time derivatives
• Eigenfunction decomposition methods
• Contaminant transport simulation
• Numerical approximation strategies

Main Subjects

• Modeling and Simulation

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