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<p>This paper presents consistent finite-volume schemes for the two-dimensional Bevilacqua–Galeão–Costa (BGC) anomalous diffusion equation on a uniform structured grid. Custom compact stencils are used to discretise the biharmonic operator in both interior and boundary control volumes, ensuring conservative spatial operators. A von Neumann stability analysis compares fully implicit and explicit time integrations, while verification via the method of manufactured solutions confirms second-order spatial and first-order temporal accuracy. Transient simulations across a range of retention factors demonstrate how the fourth-order term influences anomalous diffusion behaviour.</p>

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Finite volume solution of integer order anomalous diffusion

  • 期刊论文

  • 发表日期：

    2026年2月11日

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

摘要

This paper presents consistent finite-volume schemes for the two-dimensional Bevilacqua–Galeão–Costa (BGC) anomalous diffusion equation on a uniform structured grid. Custom compact stencils are used to discretise the biharmonic operator in both interior and boundary control volumes, ensuring conservative spatial operators. A von Neumann stability analysis compares fully implicit and explicit time integrations, while verification via the method of manufactured solutions confirms second-order spatial and first-order temporal accuracy. Transient simulations across a range of retention factors demonstrate how the fourth-order term influences anomalous diffusion behaviour.