A generalised complete flux scheme for anisotropic advection-diffusion equations (Q2026103)

The authors present a generalised CF (Complete Flux) scheme for anisotropic advection-diffusion problems. The main new feature of the method is the splitting of the diffusive and advective components of the flux, which allows for a combination of different numerical discretisations with the CF method. This allows to deal with anisotropic diffusion tensors. In particular, a combination of the HMM (Hybrid Mimetic Mixed) method and the CF method, in order to utilise the advantages of each of these methods, is explored. The main feature of HMM is that it allows to deal with 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.