A generalised complete flux scheme for anisotropic advection-diffusion equations

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Abstract

In this paper, we consider separating the discretisation of the diffusive and advective fluxes in the complete flux scheme. This allows the combination of several discretisation methods for the homogeneous flux with the complete flux (CF) method. In particular, we explore the combination of the hybrid mimetic mixed (HMM) method and the CF method, in order to utilise the advantages of each of these methods. The usage of HMM allows us to handle anisotropic diffusion tensors on generic polygonal (polytopal) grids, whereas the CF method provides a framework for the construction of a uniformly second-order method, even when the problem is advection dominated.

Original languageEnglish
Article number19
Number of pages26
JournalAdvances in Computational Mathematics
Volume47
DOIs
Publication statusPublished - 16 Feb 2021

Keywords

  • Advection-diffusion equations
  • Anisotropic diffusion
  • Complete flux scheme
  • Finite volume methods
  • Grid-based Péclet number

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