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<p>This study presents a high-precision analysis of the Bi-Flux Diffusion Model using the Generalised Integral Transform Technique (GITT). The Bevilacqua–Galeão–Costa (BGC) equation, which characterises anomalous diffusion via a dual-flux framework, is cast in dimensionless form, introducing the Bevilacqua number (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(B_v\)</EquationSource> </InlineEquation>) as the governing parameter for retention dynamics. The GITT framework is adapted to accommodate fourth-order spatial operators, incorporating a biharmonic eigenproblem and analytical filtering to rigorously enforce non-homogeneous boundary conditions. The method achieves spectral convergence in both one- and two-dimensional configurations, as verified through systematic numerical validation. Computational results confirm exponential convergence rates, even under high-gradient regimes and mixed boundary constraints, positioning GITT as a reliable benchmark for anomalous diffusion studies. The work furnishes semi-analytical modal solutions, spectral truncation criteria, and an extensible reference framework for future applications in reactive-diffusive systems and complex geometries.</p>

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Semi-analytical solutions to the bi-flux diffusion model using the generalised integral transform technique

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月4日

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  • João Flávio Vasconcellos,
  • Gisele Moraes Marinho,
  • Diego C. Knupp

摘要

This study presents a high-precision analysis of the Bi-Flux Diffusion Model using the Generalised Integral Transform Technique (GITT). The Bevilacqua–Galeão–Costa (BGC) equation, which characterises anomalous diffusion via a dual-flux framework, is cast in dimensionless form, introducing the Bevilacqua number ( \(B_v\) ) as the governing parameter for retention dynamics. The GITT framework is adapted to accommodate fourth-order spatial operators, incorporating a biharmonic eigenproblem and analytical filtering to rigorously enforce non-homogeneous boundary conditions. The method achieves spectral convergence in both one- and two-dimensional configurations, as verified through systematic numerical validation. Computational results confirm exponential convergence rates, even under high-gradient regimes and mixed boundary constraints, positioning GITT as a reliable benchmark for anomalous diffusion studies. The work furnishes semi-analytical modal solutions, spectral truncation criteria, and an extensible reference framework for future applications in reactive-diffusive systems and complex geometries.