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

Manuel Bernard (1) , Ghislain Lartigue (2) , Guillaume Balarac (1, 3) , Vincent Moureau (2) , Guillaume Puigt (4)

1 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]
2 CORIA - Complexe de recherche interprofessionnel en aérothermochimie
3 IUF - Institut universitaire de France
4 DMPE, ONERA, Université de Toulouse [Toulouse]

In 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.

Mots clés: Deconvolution; Node-Centered Finite Volume; Simplical mesh; High-order approximation; Polynomial reconstruction; Compact stencil

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Manuel Bernard, Ghislain Lartigue, Guillaume Balarac, Vincent Moureau, Guillaume Puigt. A framework to perform high-order deconvolution for finite-volume method on simplicial meshes. International Journal for Numerical Methods in Fluids, 2020, 92 (11), pp.1551-1583. ⟨10.1002/fld.4839⟩. ⟨hal-02558814v2⟩