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<p>This research presents an innovative stochastic modeling approach for simulating pollutant dispersion through fractional stochastic drift-flux (FSDF) models, combining fractional calculus with probabilistic processes to address anomalous diffusion and environmental uncertainties in heterogeneous systems. The framework employs the Karhunen-Loève expansion with a mixed noise methodology, demonstrating superior performance compared to conventional white noise simulations by achieving enhanced realism scores and capturing substantial variance with minimal computational modes for improved efficiency. Temporal fractional derivatives are discretized using the L1-algorithm, while spatial advection and diffusion components are addressed through upwind and central difference schemes, respectively. Comprehensive stability analysis, validated through energy estimation techniques, establishes the framework’s reliability across different fractional orders, with reduced fractional values promoting stability via enhanced memory effects. Computational experiments confirm the model’s precision in representing continuous source emission and natural decay processes, effectively capturing realistic concentration behavior under stochastic conditions. The FSDF model methodology provides substantial improvements for environmental risk assessment, including urban air quality evaluation, industrial emission monitoring, and stochastic environmental analysis, delivering a robust probabilistic framework for uncertainty quantification and environmental decision-making. Planned developments including multi-dimensional domain applications and real-time data incorporation are expected to broaden its utility in sophisticated environmental modeling applications.</p>

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Stochastic approaches to uncertainty quantification in fractional drift-flux models with concentration-dependent sources for pollutant dispersion

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Z. Moniri,
  • Mahmoud A. Zaky,
  • A. Babaei,
  • B. Parsa Moghaddam

摘要

This research presents an innovative stochastic modeling approach for simulating pollutant dispersion through fractional stochastic drift-flux (FSDF) models, combining fractional calculus with probabilistic processes to address anomalous diffusion and environmental uncertainties in heterogeneous systems. The framework employs the Karhunen-Loève expansion with a mixed noise methodology, demonstrating superior performance compared to conventional white noise simulations by achieving enhanced realism scores and capturing substantial variance with minimal computational modes for improved efficiency. Temporal fractional derivatives are discretized using the L1-algorithm, while spatial advection and diffusion components are addressed through upwind and central difference schemes, respectively. Comprehensive stability analysis, validated through energy estimation techniques, establishes the framework’s reliability across different fractional orders, with reduced fractional values promoting stability via enhanced memory effects. Computational experiments confirm the model’s precision in representing continuous source emission and natural decay processes, effectively capturing realistic concentration behavior under stochastic conditions. The FSDF model methodology provides substantial improvements for environmental risk assessment, including urban air quality evaluation, industrial emission monitoring, and stochastic environmental analysis, delivering a robust probabilistic framework for uncertainty quantification and environmental decision-making. Planned developments including multi-dimensional domain applications and real-time data incorporation are expected to broaden its utility in sophisticated environmental modeling applications.