Similarity and comparison of three finite-volume methods for diffusive fluxes computation on nonorthogonal meshes

Three widely used finite-volume methods for diffusive fluxes computation on nonorthogonal meshes, namely, the coordinate transformation (CT), surface decomposition (SD), and direct gradient evaluation (DGE) methods, are investigated and compared with respect to their accuracy and computational cost. The deep relationship among the three methods is revealed. If some specific choices are made, the three methods may lead to the same implicit principal fluxes when combing with the deferred correction technique. Two Poisson problems are used to examine their performances. The importance of accurate gradient evaluation method for the SD and DGE methods and accurate interpolation method for the CT method on distorted meshes is highlighted.