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.
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Acknowledgements
The authors would want to thank Prof. Sorin Pop for the discussions and comments which helped improve the presentation of the generalised local Péclet number. We would also like to thank the referees for their detailed feedback, which helped improve the overall presentation of the manuscript.
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Communicated by: Ilaria Perugia
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Cheng, H.M., Boonkkamp, J.t.T. A generalised complete flux scheme for anisotropic advection-diffusion equations. Adv Comput Math 47, 19 (2021). https://doi.org/10.1007/s10444-021-09846-x
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DOI: https://doi.org/10.1007/s10444-021-09846-x
Keywords
- Complete flux scheme
- Finite volume methods
- Advection-diffusion equations
- Anisotropic diffusion
- Grid-based Péclet number