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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 مهر 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.93661.1654

نویسندگان

Zahra Moniri¹؛ Afshin Babaei^{* 1}؛ Behrouz Parsa Moghaddam²

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

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

چکیده

‎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.

کلیدواژه‌ها

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