FOUR-POINT INTERPOLATION SCHEMES FOR CONVECTIVE FLUXES APPROXIMATION

Abstract

Two four-point interpolation schemes, FPTOI and FPFOI, have been proposed for approximating convective fluxes. In these new schemes, three points in the upstream direction and one in the downstream direction are used for interpolation. The FPTOI scheme has third-order accuracy and smaller odd truncation error terms (seventh derivative), whereas the FPFOI scheme has fourth-order accuracy and a larger critical cell Peclet number (16/5) compared with the QUICK scheme. In order to assess their capabilities, the two schemes are applied to three test problems, one linear and two nonlinear cases, all involving the simultaneous presence of convective dominance and flow-to-grid skewness. The two new schemes have high-order accuracy and further have demonstrated, in computations of flow cases, the ability to preserve better numerical stability behaviors in comparison with the QUICK scheme.