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<p>In this work, finite volume methods for the multipoint flow approximation using diamond-stencil (MPFA-D) and harmonic point-based (MPFA-H) methods are presented to approximate the pressure equation under the influence of gravitational effects in anisotropic porous media. An important contribution of this work is the explicit approximation of the gravity term in Darcy’s law, which is treated analogously to the approximation of the pressure gradient, since both terms are opposite. This approach allows the calculation of the scalar gravity at each barycenter of the computational domain, which is inserted into the flux discrete and simultaneously used to interpolate the gravity at the auxiliary points. The results confirm the effectiveness of these methods in complex flows, capturing the effects of gravity while preserving the physical properties of the system in porous media.</p>

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An accuracy study of finite volume methods of the types MPFA-D and MPFA-H for the simulation of single-phase flows under the influence of the gravity term

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • José T. G. Silva,
  • Alessandro R. E. Antunes,
  • Fernando R. L. Contreras

摘要

In this work, finite volume methods for the multipoint flow approximation using diamond-stencil (MPFA-D) and harmonic point-based (MPFA-H) methods are presented to approximate the pressure equation under the influence of gravitational effects in anisotropic porous media. An important contribution of this work is the explicit approximation of the gravity term in Darcy’s law, which is treated analogously to the approximation of the pressure gradient, since both terms are opposite. This approach allows the calculation of the scalar gravity at each barycenter of the computational domain, which is inserted into the flux discrete and simultaneously used to interpolate the gravity at the auxiliary points. The results confirm the effectiveness of these methods in complex flows, capturing the effects of gravity while preserving the physical properties of the system in porous media.