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<p>This paper investigates a new positive finite volume scheme in 3<i>D</i> to solve the anisotropic convection-diffusion equation coupled with a pressure equation of Darcy’s type. The key idea is to combine the features of the weekly monotone finite volume scheme for the diffusion part to the Scharfetter-Gummel technique, a better approximation of the convection term than the upwind version. The fluxes are designed to ensure the stability of the numerical scheme. As a result, the approximated solution remains in the physical ranges. The energy estimates are established. This strategy enables the existence of a solution to the studied finite volume scheme. The numerical section highlights that the developed solver is more robust than the standard CVFE method. The latter algorithm fails to converge whenever the data and the nonlinearities are tough because of the accumulations of undershoots over time and they end up by exploding the numerical solution. An application of this new scheme to the simulation of mass transfer in hygroscopic media is performed, with a particular focus on water imbibition in wood.</p>

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3D Scharfetter-Gummel scheme for a coupled convection-diffusion system in anisotropic porous media

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Moha Aberrah,
  • El Houssaine Quenjel,
  • Patrick Perré,
  • Mohamed Rhoudaf

摘要

This paper investigates a new positive finite volume scheme in 3D to solve the anisotropic convection-diffusion equation coupled with a pressure equation of Darcy’s type. The key idea is to combine the features of the weekly monotone finite volume scheme for the diffusion part to the Scharfetter-Gummel technique, a better approximation of the convection term than the upwind version. The fluxes are designed to ensure the stability of the numerical scheme. As a result, the approximated solution remains in the physical ranges. The energy estimates are established. This strategy enables the existence of a solution to the studied finite volume scheme. The numerical section highlights that the developed solver is more robust than the standard CVFE method. The latter algorithm fails to converge whenever the data and the nonlinearities are tough because of the accumulations of undershoots over time and they end up by exploding the numerical solution. An application of this new scheme to the simulation of mass transfer in hygroscopic media is performed, with a particular focus on water imbibition in wood.