Boundedness-Preserving Implicit Correction of Mesh-Induced Errors for VoF Based Heat and Mass Transfer

Abstract: Spatial discretisation of geometrically complex computational domains often entails unstructured meshes of general topology for Computational Fluid Dynamics (CFD). Mesh skewness is then typically encountered causing severe deterioration of the formal order of accuracy of the discretisation, or boundedness of the solution, or both. Particularly methods inherently relying on the accurate and bounded transport of sharp fields suffer from all types of mesh-induced skewness errors, namely both non-orthogonality and non-conjunctionality errors. This work is devoted to a boundedness-preserving strategy to correct for skewness errors arising from discretisation of advection and diffusion terms within the context of interfacial heat and mass transfer based on the Volume-of-Fluid methodology. The implementation has been accomplished using a second-order finite volume method with support for unstructured meshes of general topology. We examine and advance suitable corrections for the finite volume discretisation of a consistent single-field model, where both accurate and bounded transport due to diffusion and advection is crucial. In order to ensure consistency of both the volume fraction and the species concentration transport, i.e. to avoid artificial heat or species transfer, corrections are studied for both cases. The cross interfacial jump and adjacent sharp gradients of species concentration render the correction for skewness-induced diffusion and advection errors additionally demanding and has not so far been addressed in the literature.