A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

International audienceIn this paper, a new framework to design high-order approximations in the context of node-centered FiniteVolumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple andcompact differential operators, which is a critical point to achieve good performances in the High-PerformanceComputing (HPC) context. This method is based on deconvolution between nodal and volume-average valueswhich can be conducted to any order. The interest of the new method is illustrated through three differentapplications : mesh-to-mesh interpolation, levelset curvature computation and numerical scheme for convection.Higher-order can also be achieved within the present framework by introducing high-rank tensors. Althoughthese tensors feature many symmetries, their manipulation can quickly become an overwhelming task. For thisreason and without loss of generality, the present papers is limited to third-order expansion. This method,although tightly connected to thek-exact schemestheory, does not rely on successive corrections: the high-orderproperty is obtained in a single operation, which makes them more attractive in terms of performances