An efficient low dissipation finite volume scheme on unstructured grids with adaptive numerical fluxes and adaptive reconstructions

An efficient high-order finite volume scheme with adaptive numerical fluxes and adaptive reconstructions (AFAR) is proposed in this paper. The primary objective of the AFAR method is to fully leverage the advantages of existing reconstruction methods and flux schemes. A key for the design of the present AFAR method is the introduction of a new discontinuity indicator, which utilizes information from classical second-order methods and incorporates a second-layer indicator to enhance performance in cases of weak and/or contact discontinuities. This indicator will classify the mesh cells into three categories: smooth regions, weak/contact discontinuity, and shock, and the switch of the reconstruction and flux evaluation is based on the cell type. The proposed AFAR method also optimizes operational compactness and data dependence. The shock-capturing capability and high resolution of the AFAR method are demonstrated through several benchmark numerical examples.